Inclusion Criteria:

          -  All participants must meet the following criteria on screening examination to be
             eligible to participate in the study:

               -  Participants must be able to understand and willing to sign a written informed
                  consent document.

               -  Participants must be able to adhere to the dosing and visit schedules, and agree
                  to record medication times accurately and consistently in a daily diary.

               -  Participants must be at least 18 years old on day of signing informed consent.

               -  Participants must have a Karnofsky Performance Status (KPS) ≥ 70 (see Appendix
                  A).

               -  Participants must be able to swallow oral medications.

          -  Nature of illness and treatment history

               -  Participants must have histologically confirmed diagnosis of glioblastoma or
                  variants. Participants will not be eligible if the prior diagnosis was low-grade
                  glioma and a subsequent histological diagnosis of glioblastoma or variants was
                  made (e.g. secondary GBM).

               -  To be eligible for the study all participants (Cohort 1 and 2) are required to
                  provide genomic profiling data from a sequencing-based assay and must include
                  reporting of the RB1 gene in explicit terms within the report. Only sequencing
                  assays that include coverage of all exons of the RB1 gene are able to be utilized
                  (most commonly called a targeted exome assay; e.g. Oncopanel, Impact,
                  FoundationOne). In addition, patients must provide a report of copy assessment
                  which reports status of RB1. The reporting may be from a copy array (ideally
                  Oncoscan SNP array or Agilent array CGH) or can also be from sequencing assay if
                  copy status is explicitly provided with quantitative information regarding the
                  status of relevant genes.

               -  Inactivation of CDKN2A/B or C in the tumor by homozygous deletion (evidence for
                  more than single copy loss for any of the genes defined as copy array log2 ratio
                  of <0.3 by copy array; or from sequencing data with sufficient coverage for
                  evaluation). Rearrangement/evidence or intragenic breaks by copy or sequencing
                  assay also will be considered eligible for study (any copy status).

               -  Validation of wild-type RB status (no deletion/losses more than single copy by
                  copy number or sequencing data; and/or no inactivating mutations or rearrangement
                  by sequencing).

               -  Participants must be at first relapse of GBM. Relapse is defined as progression
                  following initial therapy (i.e. radiation +/- chemo if that was used as initial
                  therapy). The intent therefore is that patients had no more than 1 prior therapy
                  (initial treatment). If the patient had a surgical resection for relapsed disease
                  and no anti-cancer therapy was instituted for up to 12 weeks, and the patient
                  undergoes another surgical resection, this is considered to constitute 1 relapse.

               -  Participants must have shown unequivocal evidence for tumor progression by MRI or
                  CT scan.

                    -  For Cohort 2 subjects, CT or MRI within 14 days prior to study registration.
                       For Cohort 2, corticosteroid dose must be stable or decreasing for at least
                       5 days prior to the scan. If steroids are added or the steroid dose is
                       increased between the date of the screening MRI or CT scan and the start of
                       treatment, a new baseline MRI or CT is required.

                    -  For Cohort 1 subjects, CT or MRI should be performed ideally within 14 days
                       prior to study registration, but because the screening MRI for this subset
                       of subjects will not be used for evaluation of response, it is acceptable
                       for this MRI/CT to have been performed greater than 14 days prior to
                       registration if unavoidable. Furthermore, for this same reason, fluctuation
                       in corticosteroid dose around this MRI does not warrant repeat scan so long
                       as there is documented unequivocal evidence of tumor progression available.

               -  Confirmation of availability of sufficient tissue from a prior surgery
                  demonstrating glioblastoma or variants for correlative studies is required prior
                  to enrollment; these samples must be sent to the DFCI Coordinating Center within
                  60 days of registration.

        The following archived tissue is required for Cohort 2 patients:

        --- 20 unstained formalin fixed paraffin embedded (FFPE) sections (standard 5 micrometer
        thickness).

        The following amount of archived tissue is required for Cohort 1 patients:

          -  20 unstained formalin fixed paraffin embedded (FFPE) sections (standard 5 micrometer
             thickness)

          -  For Cohort 1 subjects, there must be > 2cm2 enhancing tissue available for resection
             and submission for study correlatives as determined by local treating team. NOTE: if
             the above-mentioned tissue is not available from the most recent surgery revealing
             GBM, participants may be enrolled with tissue available from any prior surgery
             revealing GBM with prospective approval from the Overall PI. An interval of at least
             12 weeks from the completion of radiation therapy to start of study drug unless there
             is a new area of enhancement consistent with recurrent tumor outside the radiation
             field (defined as the region outside the high-dose region or 80% isodose line) or
             there is unequivocal histologic confirmation of tumor progression.

               -  Participants must have recovered to grade 0 or 1 or pre-treatment baseline from
                  clinically significant toxic effects of prior therapy (including but not limited
                  to exceptions of alopecia, laboratory values listed per inclusion criteria, and
                  lymphopenia which is common after therapy with temozolomide).

               -  From the projected start of scheduled study treatment, the following time periods
                  must have elapsed:

          -  4 weeks or 5 half-lives (whichever is shorter) from any investigational agent;

          -  4 weeks from cytotoxic therapy (except 23 days for temozolomide; 6 weeks from
             nitrosoureas);

          -  4 weeks from antibodies;

          -  4 weeks or 5 half-lives (whichever is shorter) from other anti-tumor therapies.

          -  2 days from Novo-TTF

               -  Participants with prior therapy that included interstitial brachytherapy or
                  stereotactic radiosurgery must have confirmation of progressive disease based
                  upon nuclear imaging, MR spectroscopy, perfusion imaging or histopathology.

               -  Participants having undergone recent resection or open biopsy or stereotactic
                  biopsy of recurrent or progressive tumor will be eligible for Cohort 2 as long as
                  the following conditions apply:

          -  They have recovered from the effects of surgery.

          -  Residual disease following resection of recurrent tumor is not mandated for
             eligibility.

               -  Clinical labs - performed within 14 days prior to registration

               -  Hematology:

                    -  Leukocytes ≥ 3 K/µL

                    -  Absolute neutrophil count (ANC) ≥ 1.5 K/µL

                    -  Platelet count ≥ 100 K/µL

                    -  Absolute Lymphocyte Count ≥ 0.5 K/µL

                    -  Hemoglobin ≥ 8.0 g/dL

               -  Biochemistry:

                    -  Total serum calcium (corrected for serum albumin as needed) or ionized
                       calcium within institution's normal range, or correctable with supplements.

                    -  Magnesium within institution's normal range, or correctable with
                       supplements.

                    -  AST (SGOT) and ALT (SGPT) ≤ 2.5 x institution's ULN (or ≤ 5 X institutional
                       ULN for subjects with Gilberts syndrome)

                    -  Serum bilirubin ≤ 1.5 x institution's ULN

                    -  Serum creatinine ≤ 1.5 x institution's ULN or calculated 24-hour creatinine
                       clearance ≥ 50 mL/min

                    -  Serum amylase ≤ 1.5 x institution's ULN

                    -  Serum lipase ≤ 1.5 x institution's ULN

                    -  Serum albumin ≥ 2.5 g/dL

               -  Coagulation studies:

                    -  INR < 2.0

                    -  PTT ≤ institution's ULN, unless receiving therapeutic low molecular weight
                       heparin or oral factor Xa inhibitors.

               -  Other illnesses

                  -- Patients with prior or concurrent malignancy whose natural history or
                  treatment does not give the potential to interfere with the safety or efficacy
                  assessment of the investigational regimen are eligible for this trial.

               -  Pregnancy and Reproduction

                    -  The effects of abemaciclib and pembrolizumab on the developing human fetus
                       are unknown. For this reason, women of child-bearing potential (WOCBP) must
                       agree to use a medically approved contraceptive method during the treatment
                       period and for 120 days following the last dose of study drug. Men must
                       agree to use a reliable method of birth control and to not donate sperm
                       during the study and for at least 120 days following the last dose of study
                       drug.

                    -  Women of child-bearing potential must have a negative serum pregnancy test
                       within 7 days prior to first dose of abemaciclib.

        Exclusion Criteria:

          -  Participants who meet any of the following criteria will not be eligible for admission
             into the study.

          -  Pathology

               -  Prior evidence of 1p/19q co-deletion.

               -  IDH1/2 mutation in any prior biopsy.

               -  Tumor primarily localized to the brainstem or spinal cord.

               -  Presence of diffuse leptomeningeal disease or extracranial disease.

          -  Previous therapies

               -  Participants who have received prior treatment with a CDK4/6 inhibitor (e.g.
                  abemaciclib, palbociclib).

               -  Participants who have received anti-VEGF targeted agents (e.g. bevacizumab,
                  cediranib, aflibercept, vandetanib, XL184, sunitinib etc.).

               -  Participants who have received prior therapy with an anti-PD-1, anti-PD-L1,
                  anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4
                  (CTLA-4) antibody (including ipilimumab or any other antibody or drug
                  specifically targeting T-cell co-stimulation or checkpoint pathways).

               -  Participants who have received prior interstitial brachytherapy, implanted
                  chemotherapy, stereotactic radiosurgery or therapeutics delivered by local
                  injection (including intra-tumoral vaccines) or convection enhanced delivery.

          -  Concomitant medications

               -  Participants requiring treatment with high dose systemic corticosteroids defined
                  as dexamethasone > 2 mg/day or bioequivalent for at least 3 consecutive days
                  within 2 weeks of start of study drug.

               -  Participants who have received systemic immunosuppressive treatments, aside from
                  systemic corticosteroids (such as methotrexate, chloroquine, azathioprine, etc.)
                  within six months of start of study drug.

               -  Participants taking an enzyme-inducing anti-epileptic drug (EIAED):
                  phenobarbital, phenytoin, fosphenytoin, primidone, carbamazepine, oxcarbazepine,
                  eslicarbazepine, rufinamide, and felbamate. Participants must be off any EIAEDs
                  for at least 14 days prior to starting study drug. A list of EIAEDs and other
                  inducers of CYP3A4 can be found in Appendix D.

               -  Participants taking a drug known to be a strong inhibitor or inducer of isoenzyme
                  CYP3A (Appendix D). Participant must be off CYP3A inhibitors and inducers for at
                  least 7 days prior to starting study drug. NOTE: participants must avoid
                  consumption of Seville oranges (and juice), grapefruits or grapefruit juice,
                  grapefruit hybrids, pummelos and exotic citrus fruits from 7 days prior to the
                  first dose of study drug and during the entire study treatment period due to
                  potential CYP3A4 interaction.

               -  Participants receiving any other investigational agents.

               -  Current use of herbal preparations/medications, including but not limited to: St.
                  John's wort, Kava, ephedra (ma huang), gingko biloba, dehydroepiandrosterone
                  (DHEA), yohimbe, saw palmetto, ginseng. Participants should stop using these
                  herbal medications 7 days prior to first dose of study drug.

               -  Current use of warfarin sodium or any other coumadin-derivative anticoagulant.
                  Participants must be off Coumadin-derivative anticoagulants for at least 7 days
                  prior to starting study drug. Low molecular weight heparin and Factor Xa
                  inhibitors are allowed.

          -  Other illnesses

               -  History of allergic reactions attributed to compounds of similar chemical or
                  biologic composition to abemaciclib and/or pembrolizumab.

               -  History of intratumoral or peritumoral hemorrhage if deemed significant by the
                  treating investigator. If there are questions, the treating investigator should
                  contact the study Overall P.I., Patrick Wen, MD, at 617-632-2166.

               -  Uncontrolled intercurrent illness.

               -  Participant has an active infection requiring systemic therapy and/or known viral
                  infection (for example, human immunodeficiency virus antibodies, hepatitis B
                  surface antigen or hepatitis C antibodies).

               -  Participant with a known history of active TB (Bacillus Tuberculosis).

               -  Participant with 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 (e.g., thyroxine, insulin, or
                  physiologic corticosteroid replacement therapy for adrenal or pituitary
                  insufficiency, etc.) is not considered a form of systemic treatment.

               -  Participant with a diagnosis of immunodeficiency, including a known history of
                  Human Immunodeficiency Virus (HIV).

          -  Participants who have received a live vaccine within 30 days prior to start of study
             treatment.

             -- Participants with diarrhea ≥ CTCAE grade 2

          -  Participant has active cardiac disease including any of the following:

               -  Angina pectoris that requires the use of anti-anginal medications.

               -  Ventricular arrhythmias except for benign premature ventricular contractions.

               -  Supraventricular and nodal arrythmias requiring a pacemaker or not controlled
                  with medication.

               -  Conduction abnormality requiring a pacemaker.

               -  Valvular disease with document compromise in cardiac function.

               -  Symptomatic pericarditis.

               -  Participant has a history of cardiac dysfunction including any of the following:

                    -  Myocardial infarction within the last 6 months prior to start of study drug,
                       documents by persistent elevated cardiac enzymes or persistent regional wall
                       abnormalities on assessment of LVEF function.

                    -  History of documents congestive heart failure (New York Heart Association
                       functional classification III-IV, see Appendix I).

                    -  Documented cardiomyopathy.

                    -  Congenital long QT syndrome.

          -  Impairment of gastrointestinal (GI) function or GI disease that may significantly
             alter the absorption of abemaciclib (e.g., ulcerative diseases, uncontrolled nausea,
             vomiting, diarrhea, malabsorption syndrome, or extensive small bowel resection).
             Participants with unresolved diarrhea ≥ CTCAE grade 2 will be excluded as previously
             indicated.

               -  Participants who have undergone major systemic surgery ≤ 2 weeks prior to
                  starting study drug or who have not recovered from side effects of such therapy.

               -  Participants who are pregnant or breastfeeding.

               -  Participants with history of known coagulopathy that increases risk of bleeding
                  or a history of clinically significant hemorrhage within 12 months of start of
                  study drug or gastrointestinal bleeding or any other hemorrhage/bleeding event
                  CTCAE Grade > 3 within 6 months of start of study drug.

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