Inclusion Criteria:
 Age ≥ 6 at the time of informed consent.       2. Age ≥ 2 years to < 6 years at time of informed consent (Refer to Section 4.3):
          If PK cohort 1 is open, patients in this age range may enroll onto this cohort.
          If PK cohort 1 has been completed and deemed sufficient to proceed, then such
          patients may enroll onto the phase 2.
       3. Age ≥ 12 months to < 2 years at time of informed consent (Refer to Section
          4.3):
If PK cohort 2 is open, patients in this age range may enroll onto this cohort. If PK
cohort 2 has been completed and deemed sufficient to proceed, then such patients may
enroll onto the phase 2.
 
- -  Consent: All patients and/or their parents or legally authorized representatives
     must sign a written informed consent.
 
Assent, when appropriate, will be obtained
     according to institutional guidelines.
 
- -  Performance: Karnofsky ≥ 60% for patients > 16 years of age and Lansky ≥ 60 for
     patients ≤ 16 years of age.
 
- -  Diagnosis: Patients must enroll into one of the following cohorts:
       1.
 
Cohort A: Any type of Wilms tumor or nephroblastoma is eligible for this study
          provided they meet at least one of these criteria:
- (1) in their second or
          greater relapse, (2) refractory or in their first relapse with high risk
          histology (i.e., any anaplastic or blastemal-type after neoadjuvant
          chemotherapy), or (3) refractory or in first relapse without high risk
          histology but after having received chemotherapies other than the initial 4
          agents used as current standard of care in the up-front setting for non-high
          risk cases - specifically vincristine, dactinomycin, doxorubicin, and
          irinotecan (i.e., any patient who relapses following an initial regimen more
          intense than EE4A, DD4A, VAD, AVD, or VIVA; for example, those including
          cyclophosphamide/etoposide - such as Regimen I, M, or MVI - or those
          additionally including carboplatin - such as Regimens UH-1, UH-2, or UH-3).
 
2. Cohort B: Any Rhabdoid tumor is eligible for this cohort. This includes, but is
          not limited to, related subtypes of rhabdoid tumors such as atypical teratoid
          rhabdoid tumors (ATRT), malignant rhabdoid tumors of the kidney (MRTK),
          malignant rhabdoid tumors of the soft tissue and liver, small cell
          undifferentiated hepatoblastomas (SCUH), and small-cell carcinoma of the ovary
          of hypercalcemic type (SCCOHT). Patients must have failed to respond to at
          least.          1 line of systemic therapy prior to enrollment.
       3. Cohort C: Patients with progressive, relapsed, unresectable or metastatic
          MPNST, are eligible for this cohort. Patients must have failed to respond to at
          least 1 line of systemic therapy prior to enrollment.
       4. Cohort D: Patients must not qualify for Cohorts A, B, or C but have a solid
          tumor (no hematologic malignancies including lymphoma) for which there is
          specific evidence that this particular patient's tumor may benefit from
          selinexor.
Patients must have failed to respond to at least 1 line of systemic therapy prior to
enrollment. Examples of evidence are listed below. All patients in this cohort require
approval of study principal investigator and must provide documentation of specific
supporting evidence. i. Tumor XPO1 Dependency: Defined as either Darwin OncoTarget
demonstrating XPO1 as aberrantly activated or Darwin OncoTreat demonstrating
context-specific tumor checkpoint inversion with Selinexor, both of which must be
significant at a -log10 (Bonferroni corrected p-value) of 5 or greater. ii. Tumor XPO1
Activation: Defined as the detection of a gain of function mutation in XPO1, specifically
E571K. Additionally, detection of elevated transcriptomic or proteomic expression of XPO1
in the tumor via RNAseq or IHC, respectively, would be considered sufficient for
treatment. iii. Preclinical Tumor Testing: Defined as testing of Selinexor on patient
derived cell line, organoid, or xenograft models of the patient's tumor (or other related
tumors) performed in a laboratory context and for which, in the investigator's opinion,
demonstrates promising activity. Testing may include commercial testing as well as
academic laboratory testing.
 
- -  Disease Status: Patients on the phase II portion of the study must have measurable
     disease whereas patients on the PK cohorts can have either evaluable or measurable
     disease as measured by the revised Response Evaluation Criteria in Solid Tumors
     (RECIST) guideline (Version 1.1).
 
a. Primary Brain Tumors: Patients with primary brain tumors are eligible and must
     also have measurable disease for the phase II (as well as evaluable or measurable
     for the PK cohorts), but this can be defined as at least equal or greater than twice
     the slice thickness in two perpendicular diameters on MRI OR diffuse leptomeningeal
     disease OR clear MRI evidence of disease that may not be measurable in two
     perpendicular diameters OR positive CSF cytology alone.
 
- -  Prior Therapy: Patients must have fully recovered from the acute toxic effects of
     all prior anti-cancer therapy and meet minimum washout durations (shown below) from
     prior therapy.
 
1. Anti-cancer agents not known to be myelosuppressive: ≥ 7 days.       2. Anti-cancer and cytotoxic agents known to be myelosuppressive: ≥ 21 days.       3. Immunotherapies (including antibodies, interleukins, interferons, etc.): ≥ 21
          days.       4. Adoptive cellular therapies (including modified T cells, vaccines, etc.): ≥ 42
          days.       5. Autologous stem cell infusion (boost, no conditioning): ≥ 21 days.       6. Autologous stem cell transplantation (with conditioning): ≥ 42 days.       7. Allogeneic bone marrow transplantation: ≥ 84 days.       8. Focal external beam radiation (e.g., limited sites of disease): ≥ 14 days.       9. Substantial external beam radiation (e.g. whole lung or abdomen): ≥ 42 days.      10. Radiopharmaceutical therapy (e.g., radiolabeled antibody or MIBG): ≥ 42 days. 
- -  Hepatic Function: Adequate function (within 14 days prior to C1D1), defined as:
       1.
 
Total bilirubin < 1.5 × upper limit of normal (ULN) (except patients with
          Gilbert's syndrome, who must have a total bilirubin of <3 × ULN)
       2. Alanine aminotransferase (ALT) < 3 × ULN.       3. Serum albumin ≥ 2 g/dL. 
- -  Renal Function: Adequate function (within 14 days prior to C1D1) defined as a GFR.
 
≥ 50 ml/min/1.73 m2 determined via any of these methods:
       1. Nuclear radioisotope.       2. 24 hr urine creatinine clearance.       3. Serum cystatin c.       4. Serum creatinine using the Schwartz formula for estimating creatinine clearance
          (Schwartz et al. J Peds, 106:522, 1985)
 
- -  Hematologic Function: Adequate function (within 14 days prior to C1D1), defined as:
       1.
 
Absolute neutrophil count (ANC) ≥ 1000/mm3.       2. Platelet count ≥ 100,000/mm3.       3. Note: patients may not receive platelet transfusions nor hematopoietic growth
          factor support, including granulocyte-colony stimulating factor (e.g.
          filgrastim) and platelet stimulators (e.g. romiplostim) for at least 7 days
          prior to demonstrating adequate hematologic function.
Exclusion Criteria:
 - -  Prior Therapy: Has received selinexor or another XPO1 inhibitor previously.
 
- -  Infection: Patients who have an uncontrolled infection are not eligible.
 
Patients on
     prophylactic antibiotics or with a controlled infection within 1 week prior to C1D1
     are acceptable. 
- -  Transplants: Patients who have received allogeneic bone marrow transplant are
     potentially eligible unless they are being actively treated for GvHD.
 
Patients who
     have had a prior solid organ transplantation are not eligible.
 
- -  Compliance: Patients who as a result of serious medical, psychiatric, and/or social
     situation(s), in the opinion of the investigator, may not be able to comply with
     supportive care, safety monitoring, or any other key requirements of the study
     protocols are not eligible.
 
- -  Pregnancy and Breast-feeding: Pregnant or breast-feeding women will not be entered
     on this study because there is yet no available information regarding human fetal or
     teratogenic toxicities.
 
Pregnancy tests must be obtained in girls who are
     post-menarchal.
 
- -  Contraception: Males or females of reproductive potential may not participate unless
     they have agreed to use two effective methods of birth control, including a
     medically accepted barrier or contraceptive method (e.g., male or female condom) for
     the duration of the study.
 
Abstinence is an acceptable method of birth control.