More than discrete intrahepatic parenchymal foci of definite HCC Measureable common or main branch biliary duct involvement with HCC Patients must have confirmed hepatocellular carcinoma (HCC) by histopathology or imaging criteria according to AASLD guidelines. For HCC: Participants with a first diagnosis of HCC who have undergone a curative resection or ablation Participants are eligible to enroll if they have non-viral related-HCC, or if they have HBV-HCC, or HCV-HCC Participants previously receiving any prior therapy for HCC, including loco-regional therapies Confirmed diagnosis of hepatocellular carcinoma (HCC) HCC for which no other appropriate therapy is available. Note: Expansion Part: No prior systemic therapy for advanced/unresectable HCC Patients must have HCC limited to the liver; there must be no definitive clinical or radiographic evidence of extrahepatic HCC; portal lymphadenopathy is permitted as lymphadenopathy is commonly associated with cirrhosis unrelated to malignancy Patients with locally advanced HCC not eligible for curative therapies Have a diagnosis of hepatocellular carcinoma (HCC) and high risk for HCC recurrence Concurrent administration of systemic therapy for HCC HCC (unresectable hepatocellular carcinoma) histopathological diagnosis confirmation based on tumor tissue No prior systemic therapy for HCC Histology and/or cytology confirmed HCC per the enrolling institution; subjects in Cohort are permitted to enroll without confirmation of HCC as long as imaging Liver Imaging Reporting and Data System (LiRAD)s criteria are met and a biopsy is scheduled prior to or the day of the deb-TACE procedure; HCC confirmation must be completed prior to initiation of nivolumab for all cohorts; if a patient is found to not have confirmed HCC, they will be removed from the study Confirmed hepatocellular carcinoma (HCC) by one of the following: \r\n* Histopathology\r\n* One radiographic technique that confirms a lesion >= cm with arterial hypervascularization with washout on delayed phase COHORT B, GROUP : HEPATOCELLULAR CARCINOMA: Patients with hepatocellular carcinoma do not need to have histologic confirmation of disease as long as they meet the radiologic criteria for diagnosis of hepatocellular carcinoma (HCC) (evidence of arterial phase enhancement with corresponding venous or delayed phase wash out) Patient who has received previous systemic therapy for HCC Any prior systemic therapy for HCC Confirmed HCC based on histopathological findings from tumor tissues. Unresectable HCC with diagnosis confirmed pathologically or with noninvasive methods. Diagnosis of primary liver malignancy including hepatocellular carcinoma (HCC) or cholangiocarcinoma by characteristic imaging findings on computed tomography (CT) or MRI, clinical presentation, and/or pathologic confirmation of diagnosis; subjects with other current or prior malignancies are eligible for this study Patients must have no prior history of treatment for HCC (treatment naive). Patients must not have received prior anticancer therapy with anti-CLTA- or anti-PD for HCC. Patients receiving any concomitant systemic therapy for HCC are excluded Prior systemic therapies for HCC are allowed but not required Patients with diagnoses of hepatocellular carcinoma (HCC) according to European Association for the Study of Liver disease (EASL) criteria for diagnosis; regional lymphadenopathy will be allowed\r\n* Any virus status accepted (e.g. hepatitis C, etc.)\r\n* Any prior liver treatment Patients within unresectable HCC Patients with resectable HCC Histological or radiologic diagnosis of advanced (unresectable or metastatic) HCC with Child-Pugh A or Child Pugh B cirrhosis:\r\n* The diagnosis of HCC will be made according to the European Association for the Study of the Liver-European Organization for Research and Treatment of Cancer Clinical Practice Guidelines (EASLEORTC CPG) and according to successive modifications of the American Association for the Study of Liver Disease (AASLD) practice guidelines \r\n* Pathological diagnoses of HCC will be made according to the International Working Party criteria Cytologically or histologically confirmed advanced or metastatic HCC; if no histological diagnosis, patient must have imaging studies compatible with HCC Total maximal sum of hepatocellular carcinomas or a single conglomerate HCC > cm Measurable common or main branch biliary duct involvement with HCC Subjects with advanced hepatocellular carcinoma (HCC) with no curative option More than one line of prior systemic therapy for HCC Patients must have a diagnosis of hepatocellular carcinoma (HCC) confirmed by American Association for Study of Liver Diseases (AASLD) guidelines with a Childs-Pugh score of A or B (but, =< Childs score B)\r\n* NOTE: If the patient does not have histological confirmation of disease by biopsy, diagnosis of HCC must be documented with approval by a tumor board or other multidisciplinary conference No prior treatment of current HCC; however, recurrent HCC after resection may be included Subjects who have radiographic or histological diagnosis of hepatocellular cancer (HCC), with advanced stage disease that is not amenable to curative surgical resection; patients without histologic diagnosis must meet the radiographic criteria for HCC Histologically or cytologically confirmed hepatocellular carcinoma (HCC) or clinical diagnosis by American Association for the Study of Liver Diseases (AASLD) criteria in cirrhotic subjects is required Histological or radiologic confirmation of advanced or metastatic HCC:\r\n* The diagnosis of HCC will be made according to the guidelines of the Barcelona- European Association for the Study of the Liver (EASL) Conference (Bruix et al ) and according to successive modifications of the American Association for the Study of Liver Disease (AASLD) (Bruix et al ) \r\n* Pathological diagnoses of HCC will be made according to the International Working Party criteria (International Working Party ) Patients must have a diagnosis of hepatocellular carcinoma confirmed by at least one of the following: \r\n* Histological confirmation; \r\n* Imaging results consistent with cirrhosis and at least one solid liver lesion of > cm with early enhancement and delayed washout (American Association for the Study of Liver Diseases [AASLD] criteria for diagnosis of hepatocellular carcinoma [HCC]);\r\n* Alpha fetoprotein level > ng/mL and evidence of at least one solid liver lesion > cm, regardless of specific imaging characteristics on magnetic resonance imaging (MRI) Diagnosis of HCC: HCC is advanced, ie, treatment-refractory or metastatic, and no standard therapies are expected to be curative. Receipt of no, or of >, prior systemic drug therapies for HCC. Active malignancy other than HCC. Subjects not meeting the AASLD criteria for HCC will need a biopsy to confirm HCC prior to randomization. Have previously received therapeutic treatment for HCC outside the study protocol or is expected to receive concomitant HCC treatment prior to PFS event. Patient diagnosed with hepatocellular carcinoma in both lobes of the liver by one of the following methods\r\n* Pathologically confirmed hepatocellular carcinoma (HCC) by biopsy, OR\r\n* HCC > cm with classic radiographic findings of arterial phase enhancement with venous phase washout and pseudocapsule formation on contrast enhanced magnetic resonance imaging (MRI) or computed tomography (CT), OR\r\n* Lesion greater than cm with probable imaging features of HCC and imaging findings of cirrhosis and/or portal hypertension or a serum alpha fetoprotein (AFP) greater than ng/mL Unilobar HCC Diagnosis of unresectable intrahepatic HCC. The histopathology confirmation criterion may be waived in patients with a radiographically identifiable liver mass, known laboratory or clinical risk factors for cancer or elevated tumor markers such as alphafetoprotein (AFP)^ and clinical findings. Guidelines from the American Association for the Study of Liver Diseases (AASLD) and the European Association for the Study of the Liver (EASL) describe in detail the approach and algorithm for diagnosing HCC. Pathologically newly diagnosis HCC, which is deemed resectable and resected Histologically confirmed diagnosis of HCC No prior systemic therapy for HCC (with the exception of HCC patients enrolled in the safety run-in substudy [Japan only]) . Confirmed diagnosis of HCC by imaging criteria per American Association for the Study\n of Liver Diseases (AASLD) criteria.\n\n . Patients with single or multiple HCC who are unsuitable for surgical resection or RFA,\n but suitable for embolization.\n\n . ECOG score -. Child-Pugh score up to B.\n\n . Patients should have measurable tumor lesion(s) by contrast MRI.\n\n . Patients have adequate normal organ function and suitable laboratory criteria.\n\n . Men and women of child-bearing age need to commit to using two levels of contraception\n simultaneously to avoid pregnancy.\n\n Exclusion Criteria:\n\n . Patients who have had a liver transplantation.\n\n . Patients who have uncontrolled major medical problems such as cardiac, pulmonary (COPD\n requiring constant oxygen), renal (creatinine over .) diseases, active infectious\n diseases (except chronic Hepatitis B or C), or non-healing ulceration.\n\n . Patients who have any clinical evidence of hypoxia with O saturation less than % on\n room air.\n\n . Patients with evidence of arterial insufficiency or microangiopathy in any organ due\n to any reason, which could lead to distal extremity hypoxia, as evidenced by any\n gangrenous change in distal limbs or requiring resection for this reason.\n\n . Patients with poorly controlled HBV infection.\n\n . Patients on interferon treatment need to have at least -week washout period from Day\n .\n\n . Patients with major gastrointestinal bleeding in the prior months of enrollment or\n known diagnosis of cancer other than HCC.\n\n . Pregnant or lactating women. Patients with advanced HCC not amenable for surgical or loco-regional treatment Subject has a confirmed pathologic diagnosis of Hepatocellular carcinoma (HCC) according to the American Association for the Study of Liver Diseases (AASLD) Guidelines. Subject has received more than previous systemic therapies for Hepatocellular carcinoma (HCC). Histological or cytological confirmation of HCC (hepatocellular carcinoma) or non-invasive diagnosis of HCC as per American Association for the Study of Liver Diseases (AASLD) criteria in patients with a confirmed diagnosis of cirrhosis. Patients with hepatocellular carcinoma are eligible for this trial; hepatocellular carcinoma is defined as having at least one of the following:\r\n* Biopsy proven hepatocellular carcinoma (HCC); or\r\n* A discrete hepatic tumor(s) as defined by the Barcelona criteria for cirrhotic patients, > cm with arterial hypervascularity and venous or delayed phase washout on computed tomography (CT) or MRI Diagnosis of liver-only HCC based on European Association for the Study of the Liver (EASL) criteria (radiographic lesion appearance on contrast-enhanced computed tomography [CT] or magnetic resonance imaging [MRI], i.e. enhancement on early arterial phase, washout on portal venous phase with or without associated elevation of serum AFP level > U/ml) or histologic confirmation of HCC diagnosis, whichever is applicable Patients must have histologically diagnosed American Joint Committee on Cancer (AJCC) stage II, III, or IV HCC not eligible for curative resection, transplantation, or ablative therapies\r\n* Cases with mixed, composite, or combined HCC-cholangiocarcinoma histology are eligible with approval from study chair and provided the treating investigator believes it is in the best interest of the patient to treat the tumor with therapy targeted towards the HCC component of tumor based upon review of pathology and clinical\r\ncharacteristics Prior systemic cytotoxic therapies for HCC (chemoembolization is permitted if inclusion criteria are met) Patients must have hepatocellular carcinoma (HCC) with one of the following: \r\n* Microvascular/macrovascular invasion, \r\n* Tumor outside of Milan criteria, \r\n* Poor tumor differentiation; \r\n* Elevated surrogate markers (AFP > or PIVKA [DCP] > ) pre transplant and with biopsy proven HCC prior to orthotopic liver transplantation (OLT) or on explants Patients with local lymph node metastases\r\n* However, patients with high risk HCC who have been down-staged prior to OLT and show % necrosis on explant are eligible as long as there is biopsy proven HCC Prior use of systemic investigational agents for HCC Phase expansion: HCC Progression following at least prior systemic treatment for HCC. Receipt of more than prior systemic therapies for advanced HCC. Hepatocellular carcinoma (HCC)\r\n* Not eligible for curative attempt resection or liver transplant Locoregional therapy for hepatocellular carcinoma (HCC) must be completed at least weeks prior to the baseline scan Cohort : Participants must have hepatocellular carcinoma (HCC). These participants should have Child-Pugh stage A. Participants with HCC that: Unresectable HCC confirmed by histology or by non-invasive AASLD criteria Participants with diagnosis of HCC. Subjects must have confirmed diagnosis of unresectable HCC with any of the following criteria: Clinically confirmed diagnosis of HCC according to American Association for the Study of Liver Diseases (AASLD) criteria, including cirrhosis of any etiology or with chronic hepatitis B or C infection criteria Imaging findings for HCC corresponding to any of the following: HCC with greater than or equal to percent liver occupation Patients with the diagnosis of hepatocellular carcinoma (HCC) currently being evaluated for liver transplantation and considered for downstaging Advanced tumoral disease, defined as vascular invasion, extrahepatic spread, or diffuse HCC (% liver involvement) Subject has a documented diagnosis of advanced HCC of any etiology. Subject has a history of a non-HCC malignancy with the following exceptions: History of recurrent bacterial infections unrelated to hepatocellular carcinoma (HCC) (particularly skin or lung) Part A only: Patients with histological or cytological diagnosis of HCC who have had to prior lines of systemic therapy (progressed or intolerant to approved HCC standard of care treatment). No prior systemic therapy for HCC Advanced staged HCC (unresectable and not amenable to local or regional therapy; or metastatic HCC); the diagnosis of HCC should be based on at least one of the following:\r\n* Magnetic resonance imaging (MRI) or computed tomography (CT) consistent with liver cirrhosis AND at least one solid liver lesion measuring >= cm, with characteristics arterial enhancement and venous washout regardless of alpha-fetoprotein (AFP) levels\r\n* AFP >= ng/mL AND evidence of at least one solid liver lesion >= cm regardless of specific imaging characteristics on CT or MRI\r\n* Histological/cytology biopsy confirming HCC Histologically confirmed advanced HCC No prior systemic regimens for HCC Histological or cytological confirmation of HCC (hepatocellular carcinoma) or non-invasive diagnosis of HCC as per American Association for the Study of Liver Diseases criteria in patients with a confirmed diagnosis of cirrhosis Known to be Hepatitis B or C positive (except HCC patients) Diagnosis of HCC Diagnosis of HCC Locally advanced HCC Prior intra-arterial embolization, chemotherapy or systemic therapy for HCC. Early stage hepatocellular carcinoma (HCC) diagnosed based on the typical hallmark of HCC (hypervascular in the arterial phase with washout in the portal venous or delayed phases) Documented complete response to HCC treatment. Advanced unresectable hepatocellular carcinoma with branch portal vein thrombosis (confirmed by non-invasive criteria EASL/AASLD, mandatory by histology in non-cirrhotic patients); can be naive or recurrent HCC after curative treatment (> months before randomization) Confirmed diagnosis of HCC by histological examination or by non-invasive criteria according to European Association for the Study of the Liver (EASL) or American Association for the Study of Liver Disease (AASLD) guidelines (Part , and ). Confirmed to have HCC as described by the American Association for the Study of Liver Disease (AASLD). Histologically confirmed HCC Prior diagnosis of HCC confirmed histologically. Histologically confirmed HCC that is inoperable (where surgery is not indicated due to disease extension, co-morbidities, or other technical reasons), and not eligible for local therapy Histologically confirmed diagnosis of advanced solid tumor (dose escalation component) or metastatic melanoma (uveal or cutaneous) (doses escalation and MTD expansion components) or platinum-resistant (tumor progression within a year after the completion of platinum-based therapy) ovarian carcinoma (high grade serous, endometrial or poorly differentiated endometrioid) or HCC that has failed treatment with sorafenib or did not tolerate sorafenib or refused sorafenib, or HCC with coexistent BCT that has or has not been treated with chemotherapy, or BCT that has or has not been treated with chemotherapy. For HCC and HCC with coexistent BCT, cirrhotic status of Child-Pugh grade A-B must be present. Child-Pugh status should be determined based on clinical findings and laboratory data during the screening period (Appendix C). Subjects on anti-coagulants are to receive point for their INR status, as they are presumed to have a <. baseline PT/INR. Ovarian cancer, or HCC, or HCC with coexistent BCT, or BCT only tissue either from an archived specimen or from a new biopsy of sufficient amount and quality should be available for IHC determination of ASS status to be performed retrospectively for the ovarian cancer, or HCC, or HCC with coexistent BCT, or BCT only cohorts. Subjects with no tissue available would require a biopsy. First line advanced HCC (i.e., no prior systemic therapy) Histopathological confirmation of carcinoma in the setting of clinical and radiological characteristics which, together with the pathology, are highly suggestive of a diagnosis of HCC Hepatocellular Carcinoma (HCC) --Histologic or cytologic diagnosis of hepatocellular carcinoma HCC diagnosed by tissue or imaging study Unresectable HCC without extrahepatic disease based on CT No prior systemic therapy for HCC Patients with hepatocellular carcinoma (HCC) are eligible for this trial; HCC is defined as having at least one of the following:\r\n* HCC diagnosed either on biopsy or based on standard imaging criteria on contrast enhanced computed tomography (CT) or magnetic resonance imaging (MRI) (arterial enhancement with washout and pseudocapsule); or\r\n* A discrete hepatic tumor(s) as defined by the Barcelona criteria for cirrhotic patients, > centimeter (cm) with arterial hypervascularity and venous or delayed phase washout on CT or MRI\r\n* Presentation at multidisciplinary liver tumor board to assess eligibility for either SBRT or MWA The foci of HCC must be in an anatomic location amendable to treatment by both MWA and SBRT Patients with or more foci of HCC A diagnosis of HCC based on histopathologic findings, or a diagnosis of cirrhosis and a tumor with classical HCC imaging characteristics. Only participants found to express high levels (immunohistochemistry [IHC] score and above) of gamma-OHPdG (gamma-OHPdG-high hepatocellular carcinoma [HCC]) in baseline liver biopsy will be enrolled to receive Polyphenon E treatment Participant has confirmed HCC by CT/MRI; participants who have previously had HCC but have been treated and have been recurrence free for years are eligible Scheduled for TACE treatment of a hepatocellular carcinoma (HCC) mass (lesions reported as Liver Imaging Reporting and Data Systems B or or Organ Procurement and Transplantation Network a or b) Have an HCC mass viewable on grayscale B-mode ultrasound Patients not eligible or scheduled for TACE of a HCC mass Subjects must have a diagnosis of hepatocellular carcinoma (HCC) and a treatment plan to undergo radioembolization therapy with Y- at Indiana University Health Hospital Patients with a known infiltrative variant of HCC Patients diagnosed with HCC, who will undergo resection or transplantation within months, as part of routine clinical care and patients diagnosed with unresectable HCC Patients with unresectable HCC undergoing systemic therapy based on clinical indication or approved drug trial; and/or undergoing clinically indicated Y radioembolization HCC PATIENTS: Patient with confirmed diagnosis of HCC, and untreated or HCC PATIENTS: Patients with suspected HCC (suspected HCC nodules should preferably be smaller than cm and preferably within cm in depth of the transducer head to minimize attenuation) and untreated or HCC PATIENTS: Patients at a higher risk of HCC undergoing a screening program by ultrasound Liver tumor diagnosed histologically as HCC or suspected of being HCC in association with serum alpha-fetoprotein level > or tumor mass with characteristics of malignancy on diagnostic imaging Cohort A: HCC with FGF amplification. Cohort B: HCC without FGF amplification. Histologically confirmed HCC, not amenable to transplant, resection or loco-regional therapy Other active malignancy besides HCC within years. Must be listed for liver transplantation with HCC exception points based on the imaging diagnosis of at least one Organ Procurement and Transplantation Network (OPTN) class HCC lesion(s) per study-defined imaging criteria (participating institutions may not enroll patients in whom the HCC diagnosis is solely based on biopsy and who do not have at least one liver lesion that meets imaging criteria for OPTN Stage , Class HCC)\r\n* Patients must meet one of the following descriptions based on imaging findings:\r\n** EITHER OPTN Class B: at least focal liver lesion(s) >= cm diameter compatible with imaging diagnosis of Stage II HCC on contrast-enhanced CT imaging and/or contrast-enhanced MRI;\r\n** OR OPTN Class A: or focal liver lesions, each between > and < cm diameter, if each is compatible with imaging diagnosis of HCC on contrast-enhanced CT imaging and/or contrast-enhanced MRI\r\n** Imaging findings at the patient level in both situations must be within the United Network for Organ Sharing (UNOS) Stage , which is Milan criteria Does not meet OPTN Class imaging criteria for HCC, even if they have biopsy-proven HCC; NOTE: Patients enrolled to the trial under the Declaration of Intent to List mechanism who fail to be listed with HCC MELD/PELD Score Exception history data on the UNOS UNET Web site within days from enrollment will come off trial and will not be counted towards target accrual Subjects must have verified unresectable hepatocellular carcinoma (HCC), diagnosed on the basis of clinical and imaging criteria Subjects must satisfy one of the following conditions pertaining to their eligibility to undergo orthotopic liver transplantation (OLT):\r\n* HCC that is within Milan Criteria, i.e., TACE is indicated as a bridge to OLT (Group I); or\r\n* HCC that is outside Milan Criteria, i.e., TACE is indicated as a means of down-staging into transplant eligibility (Group II) Subjects who have received prior treatment for HCC (prior surgical procedures not related to HCC are allowed) History of HCC or suspicious mass on imaging within months prior to ascertainment of eligibility HCC screening prior to randomization