Inclusion Criteria:

          -  Histologically confirmed diagnosis of malignant glioma by enrolling institution:

               -  WHO grade IV tumors (GBM or its variants)

               -  WHO grade III anaplastic astrocytoma or oligodendroglial tumors or

               -  WHO grade II gliomas, if MRI shows contrast enhancement

          -  Tumor recurrence after previous treatment, which must have included at least radiation
             therapy and one cytotoxic chemotherapy. There is no limit on number of previous
             recurrences or lines of treatment.

          -  Previously obtained tumor sample exhibits a hypermutator phenotype. For the purposes
             of this trial, a hypermutator phenotype is defined as tumors harboring 30 mutations
             (non-synonymous somatic point or indel mutations) detected by the MSK-IMPACT or
             comparable next generation sequencing performed in a CLIA environment. Contingent to
             approval by the MSK Principal Investigator, patients with less than 30 mutations may
             be eligible if they display a mutation in a mismatch repair gene or other mutations in
             genes known to be associated with hypermutator phenotypes or microsatellite
             instability, including but not limited to MLH1, MSH2, MSH6, PMS2, POLE, POLD as
             determined by validated methods, or if microsatellite instability is present, as
             identified by polymerase chain reaction (PCR) or other validated methods.

             *Note: The MSK-IMPACT (Integrated Mutation Profiling for Actionable Cancer Targets)
             assay is a next generation genomic profiling performed on formalin-fixed,
             paraffin-embedded (FFPE) tumor tissue in a CLIA-certified Molecular Diagnostic Service
             laboratory. IMPACT provides full exon coverage of 410 cancer related genes and can
             detect base substitutions, small indels, copy number alterations and selected gene
             re-rearrangements. In some cases, additional assays such as Sanger Sequencing or
             fluorescence in situ hybridization (FISH) may be required to confirm specific results
             detected on IMPACT. Patients at MSK will have this assay to determine eligibility. Use
             of other validated next-generation sequencing techniques for eligibility may be
             considered, provided they are performed in a CLIA-certified laboratory and are
             approved by the MSK Principal Investigator.

          -  Be willing and able to provide written informed consent/assent for the trial.

          -  Be ≥ 18 years of age on day of signing informed consent.

          -  An interval of ≥ 12 weeks from the end of prior radiation therapy is required unless
             there is either: i) histopathologic confirmation of recurrent tumor, or ii) new
             enhancement on MRI outside of the radiation treatment field

          -  An interval of ≥ 4 weeks after the last administration of any investigational agent or
             any other treatment prior to first dose of pembrolizumab

          -  Must have recovered (i.e., ≤ Grade 1 or at baseline) from adverse events of any
             previous treatment. Note: Surgical resection for recurrent tumor prior to enrollment
             is allowed.

          -  Karnofsky performance status of ≥ 70

          -  Demonstrate adequate organ function as per below. All screening labs should be
             performed within 14 days of treatment initiation.

               -  Absolute neutrophil count (ANC) ≥1,500 /mcL

               -  Platelets ≥100,000 / mcL

               -  Hemoglobin ≥9 g/dL or ≥ 5.6 mmol/L without transfusion or EPO dependency (within
                  7 days of assessment)

               -  Serum creatinine ≤1.5 X upper limit of normal (ULN) OR measured or calculated
                  creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≥ 60
                  mL/min for subject with creatinine levels > 1.5 X institutional ULN

               -  Serum total bilirubin ≤ 1.5 X ULN OR direct bilirubin ≤ ULN for subjects with
                  total bilirubin levels > 1.5 ULN

               -  AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN

               -  Albumin >2.5 mg/dL

               -  International Normalized Ratio (INR) or Prothrombin Time (PT) ≤1.5 X ULN unless
                  subject is receiving anticoagulant therapy as long as PT or PTT is within
                  therapeutic range of intended use of anticoagulants

               -  Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is
                  receiving anticoagulant therapy as long as PT or PTT is within therapeutic range
                  of intended use of anticoagulants

          -  Female subject of childbearing potential should have a negative urine or serum
             pregnancy test. If the urine test is positive or cannot be confirmed as negative, a
             serum pregnancy test will be required.

          -  Female subjects of childbearing potential should be willing to use 2 methods of birth
             control or be surgically sterile, or abstain from heterosexual activity for the course
             of the study through 120 days after the last dose of study medication (Reference
             Section 9.7.2). Subjects of childbearing potential are those who have not been
             surgically sterilized or have not been free from menses for > 1 year.

          -  Male subjects should agree to use an adequate method of contraception starting with
             the first dose of study therapy through 120 days after the last dose of study therapy.

        Exclusion Criteria:

          -  Subjects requiring escalating or chronic supraphysiologic doses of corticosteroids (>
             10 mg/d of prednisone equivalent) for control of disease at the time of registration

          -  Previous or current treatment with an anti-CTLA-4, anti-PD-1, anti-PD-L1, or
             anti-PD-L2 agent.

          -  Hypersensitivity to pembrolizumab or any of its excipients.

          -  Has a diagnosis of immunodeficiency, including Human Immunodeficiency Virus (HIV) or
             acquired immunodeficiency syndrome (AIDS)

          -  Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA
             [qualitative] is detected).

          -  Has a known history of active TB (Bacillus Tuberculosis)

          -  Has a known additional malignancy that is progressing or requires active treatment.
             Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the
             skin that has undergone potentially curative therapy or in situ cervical cancer.

          -  Has active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e.

        with use of disease modifying agents, corticosteroids or immunosuppressive drugs).
        Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement
        therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic
        treatment.

          -  Has known history of, or any evidence of active, non-infectious pneumonitis.

          -  Has an active infection requiring systemic therapy.

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the subject's
             participation for the full duration of the trial, or is not in the best interest of
             the subject to participate, in the opinion of the treating investigator.

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial.

          -  Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the trial, starting with the pre-screening or screening visit
             through 120 days after the last dose of trial treatment.

          -  Unable to undergo MRI of the brain (i.e. pacemaker or any other contraindication for
             MRIs).

          -  Has received a live vaccine within 30 days of planned start of study therapy. Note:
             Seasonal influenza vaccines for injection are generally inactivated flu vaccines and
             are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live
             attenuated vaccines, and are not allowed.

          -  Has previously received treatment with bevacizumab