Suitable for breast conserving surgery and radiotherapy The interval between the last surgery for breast cancer (including re-excision of margins) and randomization must be no more than days Clinical T-Tc, any N, M invasive breast cancer, by American Joint Committee on Cancer (AJCC) th edition clinical staging, with the goal being surgery to complete excision of the tumor in the breast and the lymph node\r\nPrimary tumor must be:\r\n* Palpable\r\n* Its largest tumor diameter is > . cm by physical examination or by radiological assessment\r\n* Bi-dimensional measurement by tape, ruler or caliper technique must be provided\r\n** Note:\r\n*** Patients with contralateral ductal carcinoma in situ and/or invasive breast cancer are not eligible\r\n*** Patients with multi-focal breast cancer (defined as more than one lesion of invasive breast cancer in the same breast separated from the dominant breast lesion by less than cm of radiologically normal breast tissue) are eligible; if the other lesions have been biopsied (biopsy not required) they must meet the estrogen receptor/human epidermal growth factor receptor (ER/HER) eligibility requirements; research biopsies and Ki assessment and radiological measures are to be performed on the dominant breast lesion Inflammatory breast cancer defined as clinically significant erythema of the breast and/or documented dermal lymphatic invasion (not direct skin invasion by tumor or peau dorange without erythema) An excisional biopsy of this breast cancer Overall geometry (eg, breast size if intact breast) precludes the ability to achieve dosimetric requirements \r\n* Note: Set-up devices for breast positioning are permitted Expanded Cohort: must have breast cancer. For Part A dose confirmation: All participants must have histological evidence of advanced or metastatic soft tissue sarcoma or breast cancer. Breast cancer participants must have prescreened mutations, amplification, or gene/protein expression alterations related to Notch pathway. Patients must have the clinical diagnosis of inflammatory breast cancer as evidenced by the onset of signs and symptoms noted below within a month time-period:\r\n* Erythema of the breast\r\n* Edema of the skin of the breast\r\n* Enlargement of the breast Patients with inflammatory breast cancer are eligible if they meet both of the following criteria:\r\n* Patient has an underlying, clinically palpable breast mass of at least cm, AND\r\n* A corresponding lesion is visualized on mammogram or ultrasound Presence of microinvasion, or invasive breast carcinoma with extensive intraductal component (EIC) . Presence of multifocal and/or multicentric in breast cancer . Presence of multifocal calcifications . Presence of prior or concurrent neoadjuvant chemotherapy for breast cancer Metastatic non-gynecologic or breast primaries PIKCA MUTANT AND WILD TYPE COHORT (closed //): Evidence of inflammatory cancer (clinical presentation of skin erythema involving more than one third of the breast or pathological evidence of dermal lymphatic involvement) FNA alone to diagnose the breast cancer. Healthy women age - years with either heterogeneously dense (C) or extremely dense (D), breast tissue on D mammography, based on American College of Radiology (ACR) Breast Imaging-Reporting and Data System (BI-RADS) fifth edition classification) in either breast within months prior to randomization. Mammogram with BI-RADS final assessment category or (negative or benign findings). Cancer patients with stage -III breast cancer (BrCA) treated with breast conserving surgery or mastectomy and clear margins will be recruited to the study Patients must have one or more of the following characteristics and be eligible for breast or chest wall with or without regional nodal radiotherapy:\r\n* Prior chemotherapy for breast cancer\r\n* > cm of breast separation (the largest distance on an axial slice of the planning computed tomography [CT] simulation scan between the entry and exit points of the radiation beam on the body)\r\n* Non-Caucasian race\r\n* Requiring regional nodal irradiation without evidence of N disease Patients with stage II-III breast cancer are eligible if they are deemed appropriate for neoadjuvant endocrine therapy by the referring or treating medical oncologist. Patients with stage I disease are eligible if they are deemed borderline candidates for breast conservation and the treating surgeon recommends preoperative therapy to increase the chances of breast conservation. Patient has elected breast-conserving surgery (BCS) as surgical treatment for early-stage breast cancer Patients must meet one of the following criteria:\r\n* Pre-pathology cohort: Patient has new diagnosis of breast cancer and has elected BCS; these patients must be consented prior to the scheduled BCS with precision breast IORT; BCS (either primary breast surgery or re-excision) will occur one same date as precision breast IORT\r\n* Post-pathology cohort: Patient was previously treated for breast cancer with BCS; precision breast IORT will occur as a separate procedure within days of breast surgery; these patients should be consented after they have completed the initial excision and histological confirmation of eligibility For patients in the post-pathology stratification, precision breast IORT must be delivered within days of the last breast cancer surgery (not axillary) Note: Multicentric breast cancer and Paget's disease of the nipple are permitted. Breast cancer:\r\n* Patients inappropriate for standard breast conservation therapy (multicentric disease, inability to achieve clear margins)\r\n* Male patients with breast cancer\r\n* Autoimmune disorders, including systemic lupus erythematosus (SLE), scleroderma, etc\r\n* Distant metastases Presence of a clip in the primary breast cancer Multicentric breast cancer, defined as discontiguous tumors separated by at least cm of uninvolved tissue or discontiguous tumors that are located within separate breast quadrants either clinical or mammographically Multifocal breast cancer, defined as discontiguous discrete foci of invasive carcinoma, separated by uninvolved intervening tissue, but within an overall span of cm, or within the same breast quadrant Planning to remain on current breast cancer therapy for at least weeks Histologically confirmed breast cancer (infiltrating ductal or lobular breast carcinoma) with evidence of measurable metastatic disease; metastatic disease must be biopsy proven\r\n* Since histologic type, lymphatic permeation, blood vessel invasion, and degree of anaplasia may be prognostic variables, appropriate slides of the primary lesion will be requested for future review; HER, estrogen, and progesterone receptor positivity will be recorded Breast implant on the side of the body that will receive HIFU application Multicentric cancer in the ipsilateral breast as diagnosed by clinical examination, imaging, or pathologic assessment, not amenable to excision with negative margins with a single lumpectomy Confirmed diagnosis of inflammatory breast cancer according to international consensus criteria: () onset: rapid onset of breast erythema, edema, and/or peau dorange, and/or warm breast, with or without an underlying breast mass () duration: history of such findings no more than months () extent: erythema occupying at least / of whole breast () pathology: pathologic confirmation of invasive carcinoma Patients with breast tissue expanders must have those removed before enrollment Breast cancer suitable for mandatory baseline core biopsy Excisional biopsy or lumpectomy for the current breast cancer Tumor must be confined to either the breast or to the breast and ipsilateral axilla (Note: subjects with multifocal/multicentric tumors are eligible). Subject must have (according to TNM th edition rules): Multifocal disease within the breast Has confirmed inflammatory breast cancer by using international consensus criteria:\r\n* Onset: Rapid onset of breast erythema, edema and/or peau dorange, and/or warm breast, with/without an underlying breast mass.\r\n* Duration: History of such findings no more than months.\r\n* Extent: Erythema occupying at least / of whole breast.\r\n* Pathology: Pathologic confirmation of invasive carcinoma. Patient desires breast conserving therapy Inflammatory breast cancer defined as clinically significant erythema of the breast and/or documented dermal lymphatic invasion (not direct skin invasion by tumor or peau dorange without erythema) History of therapeutic irradiation to the breast, lower neck, mediastinum or other area in which there could potentially be overlap with the affected breast Patients must have histologically or cytologically confirmed stage IV breast carcinoma with a previous clinical diagnosis of IBC based on the presence of inflammatory changes in the involved breast, such as diffuse erythema and edema (peau dorange), with or without an underlying palpable mass involving the majority of the skin of the breast; pathological evidence of dermal lymphatic invasion should be noted but is not required for diagnosis Patients must have invasive breast cancer (IBC), confirmed according to international consensus criteria:\r\n* Onset: Rapid onset of breast erythema, edema, and/or peau dorange, and/or warm breast, with or without an underlying breast mass\r\n* Duration: History of such findings no more than months\r\n* Extent: Erythema occupying at least / of whole breast\r\n* Pathology: Pathologic confirmation of invasive carcinoma For LY + abemaciclib in HR+, HER- breast cancer: gBRCAm HER-negative metastatic breast cancer (module ) Family history: one or more close blood relative with ovarian carcinoma at any age or breast cancer age or younger or two relatives with breast, pancreatic or prostate cancer (Gleason or higher) at any age, or patients with Ashkenazi Jewish ancestry; however, patients with previously identified genetic aberrations that are associated with homologous recombination deficiency (HRD) will be eligible even in the absence of family history [e.g. somatic BRCA mutation, Fanconi anemia gene, ATM or RAD mutations] Patients may not be on an inhibitor of breast cancer resistance protein (BCRP)\r\n* NOTE: AZD is an inhibitor of breast cancer resistance protein (BCRP); the use of statins including atorvastatin which are substrates for BCRP are therefore prohibited and patients should be moved on to non-BCRP alternatives Presence of an infection including ulcerations and fungal infections in the breast to be studied Disease that cannot be measured and/or accurately followed by mammogram and/or breast ultrasound and/or dedicated breast MRI Breast preservation candidates (no prior breast or nodal radiotherapy, no imaging evidence of multicentric disease preventing resection through a single incision, no pregnant women, and no comorbid conditions precluding surgery) Outside breast imaging will be reviewed at Duke to confirm that findings are consistent with trial eligibility Breast preservation candidates (no prior breast or nodal radiotherapy, no imaging evidence of multicentric or multifocal disease, no pregnant women, and no comorbid conditions precluding surgery) Outside breast imaging will be reviewed at Duke to confirm findings are consistent with trial eligibility Breast implant in the breast to be treated with stereotactic body radiation therapy (SBRT) Has histological confirmation of HER normal breast carcinoma with a clinical diagnosis of IBC based on presence of inflammatory changes in the involved breast, including diffuse erythema and edema (peau dorange), with or without an underlying palpable mass involving the majority of the skin of the breast; pathological evidence of dermal lymphatic invasion should be noted but is not required for diagnosis of inflammatory breast cancer regardless estrogen receptor (ER)/progesterone receptor (PR) status; OR has histological confirmation of triple negative breast carcinoma (HER normal, ER/PR < %) without clinical diagnosis of IBC Hormone unresponsive breast cancer Physical and emotional ability to undergo baseline and follow-up breast MRIs and serial breast cosmesis analysis Patients must have undergone breast-conserving surgery The patient must be enrolled on the study within days following the last surgery for breast cancer (lumpectomy, re-excision of margins, or axillary staging procedure) Patients with synchronous bilateral breast cancers who will be treated with radiotherapy to each breast are eligible, provided such treatment can be performed in a manner that avoids overlap between treatment fields; both sides may be treated with accelerated partial breast irradiation (APBI) if the pathologic eligibility criteria are met for both tumors, or only one side may be treated with APBI if the criteria are met for only one tumor Patients with a history of prior breast cancer in the opposite breast are eligible as long as treatment can be performed without overlapping any prior radiation therapy (RT) fields Patient must have > . cm residual in-breast cancer and/or clinically positive residual nodal disease For HER+ breast cancer participants in parts A, C, and F: participants may receive concurrent treatment (ongoing or initiated simultaneously with abemaciclib) with IV trastuzumab. Unifocal or multifocal (confined to one quadrant, lesions less than cm apart) breast cancer ( or foci which can be encompassed by one lumpectomy) Patients with proven multicentric carcinoma (tumors in different quadrants of the breast or tumor separated by at least cm) with other clinically or radiographically suspicious areas in the ipsilateral breast unless confirmed to be negative for malignancy by biopsy Subareolar location (cancer is directly and completely under the nipple/areolar complex) of breast abnormality. Previous breast surgery with the exception of biopsy Undergoing autologous breast reconstruction Patient has metastatic breast cancer that is not suitable for surgery or radiation therapy for local disease control at the time of screening. Patients who have received more than weeks of tamoxifen therapy for this malignancy; patient who have received tamoxifen or raloxifene for purposes of chemoprevention (e.g. breast cancer prevention trial or for other past indications (including previous breast cancer) are eligible; tamoxifen or raloxifene therapy will be discontinued at least one month before the patient is enrolled on this study Patient has confirmed HER-negative advanced breast cancer (aBC) Breast tumor must be >= . cm in maximum diameter by clinical or any radiologic measurement, if node negative; if node is positive by biopsy, study participant will be eligible regardless of the size of the breast primary; in case of inflammatory breast cancer, the extent of inflammation/erythema can be used as measurable lesion Surgical treatment of the breast must have been lumpectomy; the margins of the resected specimen must be histologically free of tumor (negative surgical margins per National Surgical Adjuvant Breast and Bowel Project [NSABP] criteria) Metastatic breast cancer: limited to the subset of patients with intact breast, locally advanced tumor and involved ipsilateral supraclavicular nodes FNA alone to diagnose the breast cancer Centrally assessed Ki-, pRB, and Cyclin D status assessed preferably on post-neoadjuvant residual invasive disease of the breast, or if not possible, of residual nodal invasion or core biopsy. In case of bilateral breast cancer, tumor tissue of both sides needs to be assessable. Uncommon or rare subtypes of breast cancer. Radiologic/objective evidence of breast cancer recurrence or progression while on or within months of the end of adjuvant treatment with an AI, or progression while on or within month of the end of prior AI treatment for locally advanced or metastatic breast cancer Proven multicentric carcinoma (tumors in different quadrants of the breast, or tumors separated by at least cm) with other clinically or radiographically suspicious areas in the ipsilateral breast unless confirmed to be negative for malignancy by biopsy Unsatisfactory breast for HG-PBI as determined by the treating physician; for example, if there is little breast tissue remaining between the skin and pectoralis muscle after surgery, treatment with HG-PBI is technically problematic Time between final definitive breast procedure to HG-PBI simulation is greater than weeks If multifocal breast cancer, then it must be able to be resected through a single lumpectomy incision Alternatively, if Miller-Payne or RCB grading is not available, the patient will be eligible if the pathology report indicates that the area of residual invasive disease in the breast measures at least cm following preoperative therapy. The presence of DCIS without invasion does not qualify as residual disease in the breast. Inflammatory breast cancer defined as clinically significant erythema of the breast and/or documented dermal lymphatic invasion (not direct skin invasion by tumor or peau dorange without erythema) An excisional biopsy of this breast cancer Participants with radiologic/objective evidence of breast cancer recurrence or progression while on or within months after the end of adjuvant treatment with an AI, or progression while on or within month after the end of prior AI treatment for locally advanced or metastatic breast cancer Planning to undergo breast-conserving surgery Surgical treatment of the breast must have been lumpectomy Normal mammogram of the contralateral breast within the past months, defined as no new suspicious calcifications or other abnormal findings warranting a breast biopsy PHASE II: Patients must have the clinical diagnosis of inflammatory breast cancer as evidenced by the onset of signs and symptoms noted below within a month time-period:\r\n* Erythema of the breast\r\n* Edema of the skin of the breast\r\n* Enlargement of the breast Breast > grams or < grams in predicted weight; breast includes the breast tissue and in cases where the patient already has cosmetic breast implants, the additional breast implant mass; the sum total must be > g and < g Residual invasive disease in the breast measuring at least cm. The presence of DCIS without invasion does not qualify as residual disease in the breast. Partial breast irradiation must be scheduled to begin less than days from the last breast surgical procedure Patients with squamous or sarcomas of the breast If a patient has HER-positive breast cancer, herceptin and pertuzumab will be given along with taxane therapy Patients must have the clinical diagnosis of inflammatory breast cancer as evidenced by the onset of all signs and symptoms noted below within a month time-period:\r\n* Erythema of the breast\r\n* Edema of the skin of the breast\r\n* Enlargement of the breast Patients for whom radiotherapy would be recommended for breast cancer treatment but for whom it is contraindicated because of medical reasons Participants must have completed definitive breast surgery (mastectomy or breast-conserving) +/- reconstructive surgery with referral for definitive chest wall radiation therapy; patients with breast reconstruction are eligible if it determined by the referring or treating radiation oncologist that plan would be suboptimal without manipulation of breast implants; for patients without reconstruction, they must meet eligibility by having unfavorable cardiac anatomy defined as >= % of the heart receives >= Gy and/or left anterior descending (LAD) receives >= Gy with conventional planning; participants do not need to have measurable disease; most patients will not have measurable disease at the time of treatment Patients with multicentric gross disease defined as tumors in different quadrants of the breast or tumor separated by at least cm or other clinically or radiographically suspicious areas in the ipsilateral breast unless confirmed to be negative for malignancy or biopsy Patients who have received agents that modulate or downregulate the estrogen receptor for breast cancer prevention (e.g. tamoxifen, raloxifene, fulvestrant) or bone health (raloxifene) are eligible if they were on treatment for at least months, did not have a diagnosis of breast cancer on the medication, and have discontinued the agents months prior to study registration Treatment with breast conserving surgery Final criteria for eligibility established after simulation: the tumor bed can be readily visualized on simulation computed tomography (CT) and is localized to one quadrant or region of the breast that is amenable to partial breast irradiation Systemic chemotherapy prior to final breast conserving surgery History of therapeutic irradiation to the breast, lower neck, mediastinum or other area in which there could potentially be overlap with the affected breast Clinical diagnosis of IBC (presence of inflammatory changes in the involved breast, including diffuse erythema, heat, ridging, and peau d'orange) Breast cancer with metastasis to skeletal sites only Patients must have HER-positive breast cancer as defined by ASCO/CAP guidelines that is confirmed by a Sponsor-designated central laboratory Have histological confirmation of breast carcinoma with a clinical diagnosis of IBC based on presence of inflammatory changes in the involved breast, including diffuse erythema and edema (peau dorange), with or without an underlying palpable mass involving the majority of the skin of the breast; pathological evidence of dermal lymphatic invasion should be noted but is not required at diagnosis Evidence of metastatic breast cancer following a standard tumor staging work-up Subjects unfit for breast and/or axillary surgery (complete fixation of tumor, skin infiltration, erythema of the breast, and/or ulceration) Evidence of inflammatory cancer (clinical presentation of skin erythema involving more than one third of the breast or pathological evidence of dermal lymphatic involvement) Previous excisional biopsy of the breast cancer Multicentric breast cancer (two foci of known cancer in the breast separated by greater than cm, or in separate quadrants With advanced breast cancer whose disease was refractory to previous letrozole or anastrozole Breast cancer metastatic to the pleura that extends outside of the pleura requiring immediate therapy Patient has Tc-T, any N, M, operable breast cancer Multicentric breast cancer Primary breast cancer that is suitable for baseline core biopsy. Patients must have histologically or cytologically confirmed breast carcinoma with a clinical diagnosis of IBC based on the presence of inflammatory changes in the involved breast, such as diffuse erythema and edema (peau dorange), with or without an underlying palpable mass involving the majority of the skin of the breast; pathological evidence of dermal lymphatic invasion should be noted but is not required for diagnosis For participants with breast cancer: HER-negative disease as defined by local clinical guidelines Prior reconstructive breast surgery, breast augmentation, mastopexy or reduction mammoplasty Treated CIS of the breast or cervix Breast feeding must be discontinued for the duration of therapy with vorinostat and the concomitantly used chemotherapy, if applicable Breast carcinoma for medical reasons not being resected Patients with current local, loco-regional relapse and/or distant metastatic breast cancer Women at high risk of breast cancer due to one or more of the following:\r\n* Carry deleterious mutations in the breast cancer, early onset (BRCA), BRCA, phosphatase and tensin homolog (PTEN), tumor protein p (TP), serine/threonine kinase (STK), or cadherin- (CDH) genes\r\n* Previous diagnosis of lobular carcinoma in situ (LCIS), atypical ductal hyperplasia (ADH) or atypical lobular hyperplasia (ALH)\r\n* Lifetime risk of % or greater as calculated by the National Cancer Institute (NCI) Breast Cancer Risk Assessment Tool or the Tyrer-Cuzick International Breast Cancer Intervention Study (IBIS) Risk Assessment Tool Multi-centric disease (histologically diagnosed cancer in two different quadrants of the breast) Operable breast cancer\r\n* Patients who are planned to undergo neo-adjuvant chemotherapy are eligible as long as they consent to an additional breast biopsy following the dietary intervention immediately prior to starting chemotherapy Planned additional surgery to the surgical breast or axilla in the next year (exception would be minor surgery to breast but not axilla such as simple tissue expander replacement or lumpectomy) Being within month (before or after) of surgery for breast cancer (including breast reconstructive surgery). Smaller surgical procedures such as implant exchange are not exclusionary. Have surgery for breast cancer or breast reconstructive surgery planned during the initial month study period. Smaller surgical procedures such as implant exchange are not exclusionary. Obese breast cancer survivors and their overweight or obese partners pT breast cancer, excised with negative margins\r\n* Low risk-pTis breast cancer, excised with negative margins\r\n* Criteria for low risk-pTis:\r\n** Screen-detected\r\n** Low to intermediate nuclear grade\r\n** =< . cm in size\r\n** Resected with negative margins at >= mm Patients should be followed in Stefanie Spielman Comprehensive Breast Center (SSCBC) High Risk Breast Clinic Any woman with biopsy proven left breast DCIS or invasive cancer who has undergone a lumpectomy and who requires whole breast irradiation to the breast alone (and not to any nodal regions) as per the treating radiation oncologist Node-negative left breast cancer Enrollment in a therapeutic intervention trial in the breast medicine service Intact breast (not surgically absent) The patient must be deemed an appropriate candidate for breast conserving therapy (i.e. not pregnant, never had radiation to the treated breast, breast size would allow adequate cosmesis after volume loss from partial mastectomy) Unable to fit into the immobilization breast cup with an adequate seal Unable to fit into the breast immobilization device due to breast size or other anatomical reason Absence of a breast reconstruction prior to RT (placement of tissue expander is sufficient for group ) Adult women (both pre-menopausal and post-menopausal women are eligible) and with a history of breast cancer or with an increased risk for breast cancer on current treatment with tamoxifen or an aromatase inhibitor with the presence of vaginal dryness or dyspareunia of sufficient severity to make the subject patient desire therapeutic intervention Subjects must be prescribed and scheduled for conventional fractionated RT without concurrent chemotherapy; bolus and intensity modulated radiation therapy (IMRT) are permitted; lymph node irradiation (i.e., internal mammary nodes, supraclavicular nodes, axillary nodes, etc) as part of their prescribed radiation therapy are permitted; conventional fractionated radiation therapy regimens eligible for study are described below:\r\n* Minimal (min) total dose: whole breast: gray (Gy); breast boost: Gy; tumor bed = whole breast +/- boost: . Gy; lymph nodes: Gy\r\n* Maximal (max) total dose: whole breast: . Gy; breast boost: Gy; tumor bed = whole breast +/- boost: . Gy; lymph nodes: . Gy\r\n* Min dose per fraction: whole breast: . Gy; breast boost: . Gy; tumor bed = whole breast +/- boost: . Gy; lymph nodes: . Gy\r\n* Max dose per fraction: whole breast: . Gy; breast boost: . Gy; tumor bed = whole breast +/- boost: . Gy; lymph nodes: . Gy\r\n* Min # of fractions: whole breast: Gy; breast boost: Gy; tumor bed = whole breast +/- boost: Gy; lymph nodes: Gy\r\n* Max # of fractions: whole breast: Gy; breast boost: Gy; tumor bed = whole breast +/- boost: Gy; lymph nodes: Gy\r\n* Min # of sessions: whole breast: Gy; breast boost: Gy; tumor bed = whole breast +/- boost: Gy; lymph nodes: Gy\r\n* Max # of sessions: whole breast: Gy; breast boost: Gy; tumor bed = whole breast +/- boost: Gy; lymph nodes: Gy Subjects with breast reconstruction prior to RT Women with breast cancer involving the skin Lymphedema in an arm as a result of surgery, chemotherapy, and/or radiation therapy for breast cancer per breast surgeon or medical oncologist Patients who have not undergone autologous tissue breast reconstruction and intend to undergo implant only breast reconstruction Patients who have a history of breast tissue expander or implant placement Patients must not have symptoms or signs of benign or malignant breast disease (e.g., bloody or clear nipple discharge, breast lump) based on physician physical exam or self breast exam; patients with breast pain are eligible as long as other criteria are met To be eligible for inclusion in the annual screening regimen one of the following three conditions must be met in addition to the eligibility criteria above:\r\n* Patients are pre-menopausal; OR\r\n* Post-menopausal aged - with any of the following three risks factors:\r\n** Dense breasts (BIRADS density categories c-heterogeneously dense or d-extremely dense), or\r\n** Family history of breast cancer (first degree relative with breast cancer), or, participant positive genetic testing for any deleterious genes that indicate an increased risk for breast cancer, or\r\n** Currently on hormone therapy; OR\r\n* Post-menopausal ages - with either of the following two risk factors:\r\n** Dense breasts (BIRADS density categories c-heterogeneously dense or d-extremely dense), or\r\n** Currently on hormone therapy Women who are undergoing screening breast MRI as per standard of care for high-risk breast cancer screening Willing to donate left-over tissue if patient undergoes a breast biopsy and/or breast surgery Participants who have received breast radiation within year prior to screening breast MRI Participants who had a percutaneous breast biopsy (to include stereotactic, tomosynthesis, or ultrasound guided) that revealed ADH. INCLUSION - PATIENT: Women presenting for breast cancer screening with either MRI or mammography: Group will consist of women who present for screening breast MRI:\r\n* Asymptomatic for breast disease\r\n* Presenting for routine breast cancer screening with MRI INCLUSION - PATIENT: Group will consist of women who presented for a screening mammogram (D or D tomosynthesis) AND who have had a biopsy recommended after diagnostic workup:\r\n* Initial presentation for routine breast cancer screening with mammogram (D or D tomosynthesis) and/or ultrasound and\r\n* Biopsy recommended after subsequent diagnostic workup (breast imaging reporting and data system [BI-RADS] or ) Recommendation for breast biopsy has been made Recent prior breast surgery or breast biopsy or cyst aspiration within the prior months Women and men with symptomatic breast lump (either by palpation or imaging) OR Have one or more first or second degree relatives with breast cancer, with at least one under the age of Have breast density assessed as >= % on a prior mammogram (Boyd ) Women with a current mammographic or clinical breast exam mass which is suspicious for breast cancer (ACR class IV), and malignancy has not been ruled out Inclusion Criteria:\n\n A. Subjects whose most recent (within months) prior mammogram interpreted as\n heterogeneously dense (ACR BI-RADS Breast Density C) or extremely dense (ACR BI-RADS Breast\n Density D) breast tissue.\n\n AND\n\n B. Subjects who are asymptomatic and scheduled to undergo routine screening mammography.\n\n OR\n\n C. Subjects scheduled for image-guided needle biopsy as a result of findings obtained\n during standard of care imaging modalities (mammography, ultrasound and/or MRI) performed\n at the clinical site that participates in the study.\n\n Exclusion Criteria:\n\n . Male by birth.\n\n . Individual is less than and greater than years old.\n\n . Contraindication to bilateral mammography or MRI.\n\n . Subjects who are unable to read, understand and execute the informed consent\n procedure.\n\n . Subjects who have had mammography, ultrasound or MRI examination performed on the day\n of the study prior to RI scan.\n\n . Subjects who are pre-menopausal and are between the th and th day after the start\n of the menstrual cycle\n\n . Subjects who have significant existing breast trauma.\n\n . Subjects who have undergone lumpectomy/mastectomy.\n\n . Subjects who have undergone breast reduction or breast augmentation.\n\n . Subjects who have undergone any other type of breast surgery, including surgical\n biopsy.\n\n . Subjects who have large breast scar / breast deformation\n\n . Subjects who have undergone a breast needle biopsy within the -week period prior to\n their intended enrollment into the study.\n\n . Subjects who have a temperature > F (.C) degrees on the day of the RI\n imaging.\n\n . Subjects who are pregnant or lactating.\n\n . Subjects with known Raynaud's Disease.\n\n . Subjects with known Mastitis.\n\n . Subjects diagnosed with epileptic seizures.\n\n . Subjects with weight > kg (~ Lbs.).\n\n . Subjects who are claustrophobic or have physical limitations that do not allow them to\n sit in the system chair for the required imaging session.\n\n . Subjects with implanted pacemaker/defibrillator, implanted venous access device\n (portacath) or other implanted devices.\n\n . Subject with kidney failure\n\n . Subject with known allergy to gadolinium\n\n . Subject with a history of multiple contrast MRI scans (more than MRI scans over the\n past two year)\n\n . Inmates ( CFR .) or mentally disabled individuals.\n\n . Subjects with a BI-RADS category (e.g. for which mammogram was performed for the\n purpose of planning cancer therapy).\n\n . Subjects currently participating in another investigational clinical study.\n\n . Subject scheduled for a biopsy due to suspicious symptomatic lump\n\n . Subjects who participated in the Validation Phase will not be able to participate in\n the Testing Phase Patients breast density must be known; patients must have mammographically dense breasts, American College of Radiology (ACR) Breast Imaging (BI)- Reporting and Data System Atlas (RADS) lexicon categories c or d (heterogeneous or extreme fibroglandular tissue) on their most-recent prior screening Patient must not have undergone breast ultrasound within months prior to randomization Patient must not have previously had molecular breast imaging (MBI, multiplexed ion beam imaging [MIBI]) Patient must not be suspected of being at high-risk for breast cancer, as defined by the American Cancer Society (ACS) breast MR screening recommendations (lifetime risk of >= -%) BREAST CANCER SURVIVORS: Will be receiving either paclitaxel (Taxol or generic) either (a) weekly (~-mg/m^) or (b) every other week (i.e., dose-dense) (~ mg/m^) Taxol for the treatment of breast cancer OR BREAST CANCER SURVIVORS: Will be receiving an anthracycline and cyclophosphamide (AC) as a part of their initial treatment for breast cancer with plans to receive Taxol either weekly (~-mg/m^) or every other week (i.e., dose-dense) (~ mg/m^); Women considered at increased risk for developing breast carcinoma (those with a lifetime risk of > % due to family history, genetic predisposition, prior radiation therapy to the chest, prior biopsy showing a high risk lesion, or personal history of breast cancer) that are being screened with breast MRI Mammograms must be read as not suspicious for breast cancer (American College of Rheumatology [ACR] class I-III); subjects with a class IV mammogram may be enrolled once they have been evaluated by a breast surgeon and there is no evidence of invasive malignancy Less than years if -year breast cancer Gail risk is >= .% Women with current mammographic or clinical breast exam mass which is suspicious for breast cancer and malignancy has not been ruled out BETA/USABILITY TESTING: Utilizing the breast cancer surveillance consortium risk calculator, women will have high -year (> .%) risk for breast cancer and high breast density (heterogeneously or extremely dense) Participants must have adequate accessible breast tissue as determined by the treating physician, consisting of one breast unaffected by invasive cancer, which has not been radiated; a history of benign core biopsy of this breast will be permitted Patients with an implant in the sampled breast Breast imaging: class I-III mammogram within months of RPFNA; if class or , must be resolved with additional procedures; if breast imaging pre and post study is performed at Kansas University Medical Center (KUMC), then volumetric assessment by Volpara software will be performed Moderate risk of developing breast cancer based on either by having at least one of following:\r\n* First or second degree relative with breast cancer age or younger\r\n* Prior breast biopsy\r\n* Prior RPFNA atypia\r\n* Estimated mammographic density of % or higher\r\n* Gail -year risk of > .% (as calculated by the National Cancer Institute [NCI] Breast Cancer Risk Assessment Tool) or a year Gail Risk of X that for age group; and/or\r\n* International Breast Cancer Intervention Study (IBIS) Breast Cancer Risk Evaluation -year relative risk of > X that for the population for age group Women at high-risk of breast cancer, as defined by one of the following:\r\n* Cytologically confirmed atypical hyperplasia\r\n* Cytologically confirmed lobular breast carcinoma in situ (LCIS)\r\n* Being a carrier for at least one of the following mutations:\r\n** BRCA and/or BRCA\r\n** TP\r\n** PTEN\r\n** CDH\r\n** PALB\r\n** ATM\r\n** CHEK\r\n* Predicted lifetime risk of breast cancer > % based on family history\r\n* Predicted -year risk of breast cancer of >= .%\r\n* Predicted -year risk of breast cancer >= .% Any newly identified breast abnormality requiring surgical excision Mammogram performed or reviewed by an Ohio State University (OSU) radiologist at the Stefanie Spielman Comprehensive Breast Center or the James Cancer Hospital within the six months prior to study enrollment that are not suspicious for breast cancer (American College of Radiology [ACR] class I-III); subjects with a class IV mammogram may be entered following a negative biopsy Must be willing to undergo fine needle aspiration of the contralateral breast for breast adipose tissue at , , , and months of the study and breast epithelial tissue samples at , and months of study Subjects with insufficient breast adipose tissue and/or parenchymal breast tissue/breast density for adequate FNA sampling as determined by clinical examination and/or mammography Elevated risk of breast cancer as defined by at least one of the following categories and have declined tamoxifen and/or raloxifene therapy: Must have at least one breast available for imaging and biopsy. A previously irradiated breast (i.e., for resected DCIS) is not evaluable for breast imaging or biopsy. a. Allow for submission of core needle breast material for future use. Breast conserving surgery and indications for whole breast radiotherapy Patients must have an unaffected, non-irradiated contralateral breast with a baseline breast density score of > % as measured by standard digital mammography (BIRADs score > ) or magnetic resonance imaging (MRI) performed within months of randomization to the study If undergoing annual screening mammography, must have been performed within months prior to baseline RPFNA and interpreted either as not suspicious for breast cancer or with any supplementary imaging performed and interpreted as not suspicious for breast cancer Breast exam interpreted as normal (not suspicious for cancer) Definition of a high risk population: \r\n* The study population will consist of women with a relative risk of developing breast cancer that is at least > x that of the general population for their age group on the basis of any of the following:\r\n** Have a known genetic mutation associated with hereditary breast cancer (including breast cancer [BRCA], BRCA, tumor protein [p], etc.)\r\n** One or more first degree relatives with breast cancer, with at least one under the age of \r\n** Two or more second degree relatives with breast cancer, with at least one under the age of \r\n** Prior biopsy diagnosing atypical lobular hyperplasia, atypical ductal hyperplasia, lobular carcinoma in situ, or ductal carcinoma in situ in the last years\r\n** Have a Gail Risk Assessment (which is based on age, race, age of menarche, age of first live birth, number of first degree relatives with breast cancer, number of breast biopsies, and presence of high risk histology on any biopsies) that is considered high risk compared to the general population: \r\n*** year Gail >= . or\r\n*** year Gail >= .%\r\n** Prior diagnosis of T or T breast cancer diagnosed within the last years, without chemotherapy or antiestrogen therapy for > six months and >= months since completion of radiation therapy, when applicable Must have had a mammogram within the months prior to study enrollment; mammograms must be read as not suspicious for breast cancer (American College of Radiology [ACR] class I-III); subjects with a class IV mammogram may be entered once they have had a negative biopsy Subjects must have had a normal mammogram or breast MRI within months prior to registration; NOTE: subjects must also have a normal breast exam on the day of the pre-intervention studies Subject has multi-centric breast cancer Upon clinical exam and pre-operative imaging by mammogram +/- MRI, two or three foci of biopsy proven breast cancer separated by >= cm of normal breast tissue; foci must include at least one focus of invasive breast carcinoma with another focus of either invasive breast carcinoma or ductal carcinoma in situ (DCIS); no more than quadrants with biopsy proven breast cancer; Note: the shortest distance between lesions must be reported on mammogram +/- MRI and eligibility criteria must be met on both, if both are obtained; Note: patient is eligible for study if lesion is not visualized on all imaging modalities (i.e., any of the lesion (s) is/are visualized on MRI but not on mammogram OR visualized on mammogram but not on MRI); ultrasound cannot be used to determine patient eligibility; eligibility to be determined by bilateral mammogram +/- MRI only; fine needle aspirate of the second or third lesion to document malignancy is allowed if the first focus is shown to be invasive by core needle biopsy; patient may remain on study if, upon pathological assessment, two or three lesions identified on pre-operative imaging represent one contiguous lesion Bilateral mammogram =< days prior to date of surgery; Note: for patients undergoing more than breast operation, this is the date of the first breast surgery for breast cancer treatment Mammogram within no more than months prior to the date of informed consent (normal/benign Breast Imaging-Reporting and Data System [BI-RADS] or ) and no further routine breast imaging planned during the course of the study ( weeks DHA/placebo) Clinical and/or radiographic evidence of residual or persistent breast cancer Bilateral breast malignancy or suspicious mass in opposite breast Patients must be undergoing breast conserving therapy No patients scheduled to receive partial breast irradiation following breast conserving surgery The imaging abnormality must have been categorized as Breast Imaging-Reporting and Data System (BIRADS) level - lesion Operable breast cancer treated with NAC undergoing either breast conservation or total mastectomy who have had a post-NAC clinical bilateral breast MRI demonstrating a complete imaging response, which is defined as no residual tumor enhancement Any woman who has completed or is nearing completion of neoadjuvant therapy for breast cancer and is scheduled for a post-NAT breast MRI and mammogram Participants must be candidates for definitive local therapy with breast conserving therapy or deemed as potential candidates following NAT (this takes into account tumor to breast size ratio appropriate for breast cancer therapy [BCT], and the ability to undergo standard radiation therapy post-operatively) Diagnosed with a Breast Imaging Reporting and Data System (BI-RADS) score of or higher breast abnormality greater than cm in size Participants must be candidates for definitive local therapy with breast conserving therapy (this takes into account tumor to breast size ratio appropriate for breast-conserving surgery [BCS], and the ability to undergo standard radiation therapy post-operatively) Known or suspected (Breast Imaging Reporting and Data System [BIRADS] on imaging) primary breast cancer At least one breast lesion that is cm or greater in size by standard imaging (e.g. mammography, ultrasound or breast magnetic resonance imaging [MRI]); only one type of imaging is required to show a lesion of cm or greater in order for the patient to be eligible to participate in this study; patients that have a prior diagnosis of primary breast cancer in the opposite breast can be included Eligible for breast conserving surgery, lumpectomy and radiation Involvement in another therapeutic trial for breast cancer at Dana Farber or elsewhere No prior history of breast reconstruction, reduction, or augmentation Known or suspected breast cancer with at least one breast lesion that is cm or greater in size by standard imaging (e.g. mammography, ultrasound or breast magnetic resonance imaging [MRI]); only one type of imaging is required to show a lesion of cm or greater in order for the patient to be eligible to participate in this study; patients that have a prior diagnosis of primary breast cancer in the opposite breast can be included PATIENT: Patients who have had prior breast reduction Patients who will receive radiotherapy as treatment for left-sided breast cancer Has biopsy-proven invasive breast cancer (Breast Imaging Reporting and Data System [BI-RADS] ) and scheduled for neoadjuvant chemotherapy (NAC) Scheduled for breast core needle or surgical biopsy of at least one breast lesion based on suspicious breast lesion (Breast Imaging Reporting and Data System [BIRADS] score of or ) from pre-study standard of care (SOC) imaging studies Scheduled for mammogram, breast ultrasound and/or breast MRI Diagnostic findings from prior mammography highly suggestive of breast malignancy (Breast Imaging-Reporting and Data System [BI-RADS] [R] category ) or known biopsy-proven malignancy (BI-RADS [R] category ) Symptomatic of any breast abnormality Recent breast biopsy Biopsy confirmed malignancy associated calcifications in at least one breast Patients with cancer > cm, clinically positive nodes, prior surgery for breast cancer in the index breast, thyroid dysfunction, hypersensitivity to iodine, and hepatic or renal insufficiency will be excluded from the study Unresected, untreated breast cancer that meets one of the following clinical stages:\r\n* T, T, or Ta-c lesion, any N, M\r\n* Note: Patients with inflammatory breast cancer (Td) are not eligible; bilateral cancers are permitted with approval of the Protocol Chair; participants with clinically evaluable disease will be followed for response by clinical examination; measurable disease is not required for participation BREAST CANCER PARTICIPANTS: Participant has biopsy proven breast cancer and may or may not undergo surgical excision of the cancerous lesion(s) BREAST CANCER PARTICIPANTS: Patient is able to remain still for duration of each imaging procedure Multicentric breast cancer Women with Breast Imaging-Reporting and Data System (BI-RADS) or Required studies include diagnostic mammogram of the affected breast within months prior to registration, and a two-view (full view craniocaudal [CC] and a full view mediolateral oblique [MLO]) mammogram of both breasts within months of registration (if the patient has only one breast, a unilateral exam of the intact breast is required) Patient desire to undergo breast conserving surgery Multicentric breast cancer, defined as two or more tumors in different quadrants of the breast Patients whose breast lesion is unequivocally a cyst by unenhanced US Patients will be identified as possible participants in the Radiology Imaging suites and Breast Surgery Clinics Women at high-risk of breast cancer with an order for a clinical screening breast MRI The primary breast tumor must be detectable by mammogram or breast ultrasound at the time of diagnosis The primary tumor is not visualized by mammogram or breast ultrasound at the time of diagnosis Have a prosthesis/implant in the operative breast The use of statins including atorvastatin are prohibited and patients should be moved on to non-breast cancer resistance protein (BCRP) alternatives Participants must have been clinically diagnosed with breast cancer and scheduled for axillary lymph node dissection (ALND) and radiation treatment at MD Anderson (receiving chemotherapy, mastectomy or breast-conserving surgery, ALND (> nodes) and radiation treatment for breast cancer, identified by Drs. Mittendorf and Shaitelman of the Nellie B. Connally Breast Cancer Center at MD Anderson) Participants must have a mammographic breast composition category (density) of c or d PHASE I: Women who state that there are still deciding on breast cancer treatment (e.g., whether or not to take hormone therapy or to receive radiation treatment) Women who () have a personal history of a single stage - breast cancer, () were recently diagnosed within the past months, and () are treated at a participating breast oncology clinic. Newly diagnosed female breast cancer patients scheduled to see one of four breast surgeons at the Huntsman Cancer Hospital Breast Surgery Clinic at the University of Utah Patients breast cancer has not recurred during the time period positive clinical breast examination Requiring chronic treatment with breast cancer resistance protein (BCRP) inhibitors. Subjects with prior breast surgeries, mastectomies, breast reconstructions or implants. (Note: subjects who have had prior breast biopsies are not excluded) Subjects with prior reduction mammoplasties or breast reductions performed less than years prior to enrollment to this study. Has completed treatment for Stage I-III breast cancer, if indicated, and ? months elapsed between the completion of treatment with curative intent (e.g., date of primary breast tumor surgery or date of last adjuvant chemotherapy administration, whichever occurred last) and first documented local or distant disease recurrence. At least prior HER-directed therapy regimens for metastatic breast cancer, including trastuzumab and TDM-.