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)Xx_NEWLINE_xXDiagnosis: * 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 diagnosisXx_NEWLINE_xXDiagnosis: * 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 therapyXx_NEWLINE_xXPart 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 metastasesXx_NEWLINE_xXPart 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-HCGXx_NEWLINE_xXPatients 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)Xx_NEWLINE_xXPatients 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)Xx_NEWLINE_xXPatients 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)Xx_NEWLINE_xXELIGIBILITY 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-HCGXx_NEWLINE_xX