Lumbar cerebrospinal fluid (CSF) cytology examination must be obtained pre-operatively or within 31 days following surgery; the optimal time for obtaining CSF is prior to surgery or 1-3 weeks following surgery; ventricular CSF (either pre- or post-op) may be used only if a post-operative spinal tap is contraindicated; if a spinal tap is contraindicated and there is no ventricular CSF available, then CSF cytology can be waived for patients with supratentorial tumors or if there is documentation of spinal subarachnoid metastases (M3); patients who are categorized as M1 must have either an intra-operative positive CSF (via lumbar puncture at the end of the procedure) or a positive lumbar CSF obtained > 7 days post-operatively Patients with non-adenocarcinomas, adenosquamous carcinomas, islet cell (neuroendocrine) tumors, cystadenomas, cystadenocarcinomas, carcinoid tumors, duodenal carcinomas, distal bile duct, and ampullary carcinomas; patients with tumors that are largely IPMN with a minimal or minor component of invasive carcinoma are not eligible; patients with acinar carcinomas are not eligible; patients with IPMNs that contain some secondary (minor) foci of adenocarcinoma are also not eligible Patients identified as needing spinal radiation at diagnosis (e.g. spinal metastasis or malignant cells identified on cerebrospinal fluid [CSF] cytology) are excluded Patients whose tumors arise in the dural and intra-dural soft tissues of the cranium and spine are not eligible Clinical T4 tumors Patients must be newly diagnosed with localized primary CNS NGGCT (Stratum 1) or localized primary CNS germinoma (Stratum 2); germ cell tumors located in the suprasellar, pineal, bifocal (pineal + suprasellar) and ventricles are eligible; tumors present in the above mentioned locations and with unifocal parenchymal extension are eligible* Stratum 1(NGGCT): Patients must have one of the following criteria:** Patients with serum and/or CSF hCGbeta > 100 mIU/mL or any elevation of serum and/or CSF alpha-fetoprotein (AFP) > 10 ng/mL or greater than the institutional normal are eligible, irrespective of biopsy results** Patients with any of the following elements on biopsy/resection are eligible, irrespective of serum and/or CSF hCGbeta and AFP levels: endodermal sinus tumor (yolk sac), embryonal carcinoma, choriocarcinoma, malignant/immature teratoma, and mixed GCT with malignant GCT elements* Stratum 2 (Germinoma): Patients must have both serum and CSF markers obtained (unless obtaining CSF is medically contraindicated) and must have one of the following criteria to be eligible:** Patients with institutional normal AFP (or =< 10 ng/mL if no institutional normal exists) in both serum and CSF (unless medically contraindicated) AND hCGbeta 5 to =< 50 mIU/mL in serum and/or CSF (unless medically contraindicated) (only 1 is required to be elevated) are eligible; no histologic confirmation required** Patients with bifocal (pineal + suprasellar) involvement or pineal lesion with diabetes insipidus (D1) AND hCGbeta =< 100 mIU/mL in serum and/or CSF AND institutional normal AFP (or =< 10 ng/mL if no institutional normal exists) in both serum and CSF (unless medically contraindicated) are eligible; no histologic confirmation required** Patients with histologically confirmed germinoma or germinoma mixed with mature teratoma and hCGbeta =< 100 mIU/mL in serum and/or CSF and institutional normal AFP (or =< 10 ng/mL if no institutional normal exists) in both serum and CSF (unless medically contraindicated) are eligible Patients must have CSF tumor markers obtained prior to enrollment unless medically contraindicated; ventricular CSF obtained at the time of CSF diversion procedure (if performed) is acceptable for tumor markers but lumbar CSF is preferred; in case CSF diversion and biopsy/surgery are combined, CSF tumor markers should be collected first Patients with tumors located outside the ventricles (basal ganglia, thalamus) are not eligible Patients with history of John Cunningham (JC) virus identified in the cerebrospinal fluid (CSF) or previous history of PML will be excluded from the study Patients with newly diagnosed DIPGs, defined as tumors with a pontine epicenter and diffuse involvement of the pons, are eligible without histologic confirmation* Patients with brainstem tumors that do not meet these criteria or are not considered to be typical intrinsic pontine gliomas will only be eligible if the tumors are biopsied and proven to be an anaplastic astrocytoma, glioblastoma, gliosarcoma, diffuse midline glioma with histone H3 K27M mutation, or anaplastic mixed glioma; patients with pilocytic astrocytoma, fibrillary astrocytoma, gangliogliomas, or other mixed gliomas without anaplasia are not eligible* Patients with disseminated disease are not eligible, and magnetic resonance imaging (MRI) of spine must be performed if disseminated disease is suspected by the treating physician* Enrollment must be no later than 28 days after the date of radiographic diagnosis or surgery, whichever is the later date Patient must be CNS (cerebrospinal fluid [CSF]) negative for leukemia Patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) Part A: Patients with relapsed or refractory solid tumors, including patients with primary or metastatic CNS tumors Histologically confirmed Rb1 positive primary recurrent, progressive, or refractory central nervous system tumors; patients with low grade gliomas are excluded Patients with low grade gliomas and Rb1 negative tumors Patients with MYCN amplified tumors are not eligible Diagnosis: * Phase 1 (Part A)** Solid tumors (Part A1): patients with relapsed or refractory solid tumors including central nervous system (CNS) tumors without bone marrow involvement are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG)** Ewing sarcoma or peripheral primitive neuroectodermal tumor (PNET) (Part A2): patients with relapsed or refractory Ewing sarcoma or peripheral PNET without bone marrow involvement will be eligible for Part A2 if there are no available slots on Part A1; these patients will be enrolled at one dose level below the dose level at which patients on Part A1 are actively enrolling, or at the starting dose level (dose level 1) if dose escalation has not yet occurred; patients must have had histologic verification of malignancy at original diagnosis or relapse* Phase 2 (Part B)** Ewing sarcoma or peripheral PNET: patients with relapsed or refractory Ewing sarcoma or peripheral PNET are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse* Phase 2 (Part C)** Acute lymphoblastic leukemias (ALL): patients must have 2nd or greater relapse of pre-B ALL or T-cell ALL; patients may not have refractory disease** Patients with ALL must have had histologic verification of the malignancy at the most recent relapse, including immunophenotyping to confirm diagnosis Patients whose primary tumors arise in the intra-dural soft tissue (eg. brain and spinal cord) are not eligible Diagnosis: * Part A: Patients with recurrent or refractory solid tumors, including lymphoma and CNS tumors, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG)* Part B: Patients with recurrent or refractory high grade glioma (World Health Organization [WHO] grade III/IV) including disseminated tumors (excluding diffuse intrinsic pontine glioma [DIPG]), not requiring surgical resection; patients must have had histologic verification of malignancy at original diagnosis or relapse* Part C: Patients with recurrent or refractory high grade glioma (WHO grade III/IV) and requiring surgical resection (excluding DIPG and disseminated tumors), who in the opinion of treating physicians, are medically stable to receive 3-4 doses of selinexor (8-10 days of treatment) before undergoing surgery without compromising the success of the procedure; note that if, in the opinion of treating physicians, current symptoms necessitate surgery before 3-4 doses will be able to be received, surgery should not be delayed to administer selinexor, and the patient would be ineligible for protocol therapy Patients must have relapsed or become refractory to conventional therapy, with a regimen including some combination of high dose methotrexate, doxorubicin, cisplatin, ifosfamide and etoposide; and have had histologic verification of osteosarcoma at original diagnosis or at the time of recurrence Part A: Patients with recurrent or refractory non-CNS solid tumors are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except patients with extra-cranial germ-cell tumors who have elevations of serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG); patients in part A cannot have CNS metastases Part B: Patients with recurrent or refractory CNS tumors will be eligible and must have a histological verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with CNS-germ cell tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-HCG Patients must have histologic diagnosis of osteosarcoma at original diagnosis Patients with distant bone metastases at original diagnosis or relapse (patients with only skip lesions will be eligible) Patients must have had histologic verification of AML at original diagnosis Patient must have negative lumbar cerebrospinal fluid (CSF) cytology; CSF cytology for staging should be performed preferably no sooner than 14 days post operatively to avoid false positive CSF; ideally, CSF should be obtained between day 14 and day 21 to allow for final staging status before enrollment onto the study* Note: patients with positive CSF cytology obtained prior to 14 days after surgery may have cytology repeated to determine eligibility and final CSF status Patients with recurrent or refractory solid tumors, including central nervous system (CNS) tumors, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or in patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) Patients with recurrent or refractory solid tumors, including central nervous system (CNS) tumors or lymphoma, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) Patients must have recurrent or refractory disease, or newly diagnosed disease with no known curative therapy or therapy proven to prolong survival with an acceptable quality of life; patients must have had histologic verification of one of the malignancies listed below at original diagnosis or at relapse:* Ewing sarcoma * Rhabdomyosarcoma (RMS)* Non-rhabdomyosarcoma soft tissue sarcomas (STS) including microphthalmia transcription factor associated STS (alveolar soft part sarcoma [ASPS] and clear cell sarcoma [CCS])* Osteosarcoma* Wilms tumor * Rare tumors ** Medullary thyroid carcinoma (MTC)** Renal cell carcinoma (RCC)** Hepatocellular carcinoma (HCC)** Hepatoblastoma ** Adrenocortical carcinoma** Pediatric solid tumors (including central nervous system [CNS] tumors) with known molecular alterations in the targets of XL184 (i.e., MET amplification, overexpression, activating mutation, MET translocation, MET exon skipping mutations, activating RET mutations, RET rearrangement, overexpression or activation of AXL); documentation of the alteration from a Clinical Laboratory Improvement Act (CLIA) certified laboratory will be required Patients with recurrent or refractory solid tumors, including CNS tumors, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) Histologically proven stage III colon adenocarcinoma (any T [Tx, T1, T2, T3, or T4], N1-2M0; includes N1C); tumors must be deemed to originate in the colon including tumors that extend into/involve the small bowel (e.g. those at the ileocecal valve) Patients with non-melanoma skin cancers (NMSC) must have advanced or refractory tumors* Advanced/unresectable is defined by at least 1 of the following criteria: tumors 2 cm or more, tumors considered unresectable, tumors invading deep tissues such as muscle, cartilage or bone, tumors showing perineural invasion, and/or tumors metastatic to loco-regional lymph nodes and/or distant sites* Refractory is defined by persistent or recurrent tumor despite prior therapy consisting of at least 1 of the following: surgery, radiation therapy, intralesional therapy, topical therapy, or systemic therapy Patients with infra-tentorial tumors are not eligible ELIGIBILITY CRITERIA FOR ENROLLMENT ONTO APEC1621SC: Patients with recurrent or refractory solid tumors (including non-Hodgkin lymphomas, histiocytoses [e.g. Langerhans cell histiocytosis (LCH), juvenile xanthogranuloma (JXG), histiocytic sarcoma], and central nervous system [CNS] tumors) are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-HCG