Inclusion Criteria:

   - Patients with a histologically confirmed diagnosis of a primary CNS tumor
   (medulloblastoma, high-grade glioma, or diffuse intrinsic pontine glioma [DIPG]) that
   is recurrent, refractory, or progressive. All tumors must have histologic verification
   at either the time of diagnosis or recurrence except patients with diffuse intrinsic
   brain stem tumors. These patients must have radiographic or clinical evidence of
   progression. Patients with a recurrent, progressive, or refractory primary CNS tumor
   with evidence of genetic activation of the MET pathway, regardless of histology, are
   also eligible to the Phase I component of this study

      - Note: Refractory disease is defined as the presence of persistent abnormality on
      conventional magnetic resonance imaging (MRI) imaging that is further
      distinguished by histology (biopsy or sample of lesion) or advanced imaging, OR
      as determined by the treating physician and discussed with the primary
      investigator prior to enrollment

   - Efficacy Expansion Cohort: Patients must have a recurrent, progressive, or refractory
   primary CNS tumor with evidence of genetic activation of the MET pathway, regardless
   of histology. Specimens can be from diagnosis or recurrence and there is no time limit
   from when the specimen was obtained prior to enrollment onto the efficacy expansion
   cohort. Results from a Clinical Laboratory Improvement Act (CLIA)-certified laboratory
   will be accepted for this eligibility criterion. Sites must provide a redacted copy of
   the local CLIA-certified sequencing laboratory report to the study chair via email
   prior to enrollment. MET pathway activation is defined as:

      - MET mutations, OR

      - MET or HGF amplification, OR

      - MET fusion

   - Recurrent or refractory primary malignant CNS tumor patients must have adequate
   pre-trial frozen or formalin-fixed paraffin-embedded (FFPE) tumor material available
   for the required correlative studies. If target amounts of tissue or number of slides
   are not available, the site must obtain study chair/co-chair approval for adequacy of
   submitted tumor samples and prioritization of studies to be performed, prior to
   patient enrollment

      - Patients with DIPG who have pre-trial tumor tissue available are requested to
      submit tissue; however, this is not required for eligibility

   - Patients must have evaluable disease to be eligible. Evaluable disease is defined as
   the presence of at least one lesion that can be measured accurately in at least 2
   (two) dimensions

   - Patients must be > 5 years and =< 21 years of age at the time of study enrollment

   - Body surface area (BSA)

      - Patients enrolled on 75 mg/m^2/day (dose level 0) must have a BSA >= 1.00 m^2

      - Patients enrolled on 150 mg/m^2/day (dose level 1) must have a BSA >= 0.55 m^2

         - Patients enrolled on 240 mg/m^2/day (dose level 2) must have a BSA >= 0.67
         m^2

      - Patients enrolled on 350 mg/m^2/day (dose level 3) must have a BSA >= 0.73 m^2

   - Patients must have failed prior standard therapy for their tumor. Patients with
   medulloblastoma must have received radiation therapy in addition to platinum and
   alkylator-based chemotherapy. Patients with high-grade glioma (HGG) and DIPG must have
   at least received radiation therapy. Patients must have recovered from the acute
   treatment related toxicities (defined as =< grade 1 if not defined in eligibility
   criteria) of all prior chemotherapy, immunotherapy, radiotherapy, or any other
   treatment modality prior to entering this study

   - Patients must have received their last dose of known myelosuppressive anticancer
   therapy at least 21 days prior to enrollment or at least 42 days if it included
   nitrosourea

   - Biologic or investigational agent (anti-neoplastic):

      - Patients must have recovered from any acute toxicity potentially related to the
      agent and received their last dose of the investigational or biologic agent >= 7
      days prior to study enrollment

         - For agents that have known adverse events occurring beyond 7 days after
         administration, this period must be extended beyond the time during which
         adverse events are known to occur

      - Monoclonal antibody treatment and agents with known prolonged half-lives:

         - Patients must have recovered from any acute toxicity potentially related to
         the agent and received their last dose of the agent >= 28 days prior to
         study enrollment

   - Patients must have had their last fraction of:

      - Craniospinal irradiation or total body irradiation or radiation to >= 50% of
      pelvis > 3 months prior to enrollment

      - Focal irradiation > 4 weeks prior to enrollment

   - Patients must be:

      - >= 6 months since allogeneic stem cell transplant prior to enrollment with no
      evidence of active graft versus (vs.) host disease

      - >= 3 months since autologous stem cell transplant prior to enrollment

   - Both males and females of all races and ethnic groups are eligible for this study

   - Neurologic Status

      - Patients with neurological deficits should have deficits that are stable for a
      minimum of 1 week prior to enrollment. A baseline detailed neurological exam
      should clearly document the neurological status of the patient at the time of
      enrollment on the study

      - Patients with seizure disorders may be enrolled if seizures are well controlled

      - Patients must be able to swallow whole tablets to be eligible for study
      enrollment

   - Karnofsky performance scale (KPS for > 16 years of age) or Lansky performance score
   (LPS for =< 16 years of age) assessed within two weeks of enrollment must be >= 50

      - Patients who are unable to walk because of neurologic deficits, but who are up in
      a wheelchair, will be considered ambulatory for the purpose of assessing the
      performance score

   - Absolute neutrophil count >= 1.0 x 10^9 cells/ L

   - Platelets >= 100 x 10^9 cells/ L (unsupported, defined as no platelet transfusion
   within 7 days prior to enrollment)

   - Hemoglobin >= 8 g/dL (hemoglobin should be unsupported, i.e., red blood cell
   transfusions are not allowed within 14 days prior to enrollment)

   - Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 2.5 x the upper
   limit of normal (ULN) with total bilirubin =< 1x ULN OR total bilirubin > ULN - =< 1.5
   x ULN with ALT and AST =< 1 x ULN

   - Albumin >= 2 g/dL

   - Serum creatinine based on age/gender. Patients that do not meet the criteria below but
   have a 24 hour creatinine clearance or glomerular filtration rate (GFR) (radioisotope
   or iothalamate) >= 70 mL/min/1.73 m^2 are eligible

      - Age: Maximum serum creatinine (mg/dL)

      - 2 to < 6 years: 0.8 (male and female)

      - 6 to < 10 years: 1 (male and female)

      - 10 to < 13 years: 1.2 (male and female)

      - 13 to < 16 years: 1.5 (male), 1.4 (female)

      - >= 16 years: 1.7 (male), 1.4 (female)

   - International normalized ratio (INR) < 1.5 x ULN and activated partial thromboplastin
   time (aPTT) < 1.5 x ULN unless patients are receiving therapeutic anti-coagulation
   which affects these parameters

   - Patients with known tumor thrombus or deep vein thrombosis are eligible if clinically
   stable on low molecular weight heparin for >= 2 weeks

   - Cardiac function:

      - Mean resting corrected QT interval (QTc Bazett) =< 450 msec on screening obtained
      from 3 electrocardiograms (EKGs)

   - Oxygen saturation as measured by pulse oximetry is > 93% on room air

   - Patients who are receiving corticosteroids must be on a stable or decreasing dose for
   at least 1 week prior to enrollment

   - Patients must be off all colony-stimulating factor(s) (e.g., filgrastim, sargramostim
   or erythropoietin) for at least 1 week prior to enrollment. Two (2) weeks must have
   elapsed if patients received polyethylene glycol (PEG) formulations

   - Pregnancy Prevention

      - Patients of childbearing or child fathering potential must be willing to use a
      medically acceptable form of birth control, which includes abstinence, while
      being treated on this study

      - Women of child-bearing potential should use effective contraception from the time
      of enrollment until 4 weeks after discontinuing study treatment

      - Male study participants should use a condom with female partners of child-bearing
      potential during the study and for 6 months after discontinuing study treatment

      - If the female partner of a male study participant is not using effective
      contraception, men must use a condom during the study and for 6 months after
      discontinuing study treatment

      - Male study participants should avoid fathering a child and refrain from sperm
      donation from study start to 6 months after discontinuing study treatment

   - Ability to understand and willingness to sign a written informed consent document.
   Legally authorized representatives may sign and give informed consent on behalf of
   study participants.

Exclusion Criteria:

   - Pregnant women or nursing mothers are excluded from this study. Female patients of
   childbearing potential must have a negative serum or urine pregnancy test within 7
   days prior to enrollment. If the urine test is positive or cannot be confirmed as
   negative, a serum pregnancy test will be required. Pregnant women are excluded from
   this study because there are unknown but potential risks to an unborn baby from
   savolitinib. Because there is an unknown but potential risk for adverse events in
   nursing infants secondary to treatment of the mother with savolitinib, breastfeeding
   should be discontinued if the mother is treated with savolitinib

   - Patients with a known serious active infection including, but not limited to, viral
   hepatitis, human immunodeficiency virus, tuberculosis

   - Patients with any clinically significant unrelated systemic illness or significant
   cardiac, pulmonary, hepatic, or other organ dysfunction), that in the opinion of the
   investigator would compromise the patient's ability to tolerate protocol therapy, put
   them at additional risk for toxicity or would interfere with the study procedures or
   results

   - Patients with uncontrolled hypertension (i.e., a blood pressure [BP] > 95th percentile
   for age, height, and gender, patients with values above these levels must have their
   blood pressure controlled with medication prior to starting study drug)

      - The normal blood pressure by height, age, and gender can be assessed by using the
      NIH Guidelines on the PBTC Member's website (Protocols- Generic Forms and
      Templates- Normal Blood Pressure by Height and Age).

   - Patients with any of the following cardiac diseases

      - Congestive heart failure (New York Heart Association >= grade 2)

      - Clinically significant cardiac arrhythmia

      - Mean resting corrected QT interval (QTc Bazett) > 450 msec on screening obtained
      from 3 electrocardiograms (EKGs) or

      - Factors that may increase the risk of QTc prolongation such as chronic
      hypokalemia not correctable with supplements, congenital or familial long QT
      syndrome, or

      - Family history of unexplained sudden death under 40 years of age in first-degree
      relatives or

      - Any concomitant medication known to prolong the QT interval and cause Torsade de
      Pointes. These drugs must have been discontinued prior to the start of
      administration of study treatment in accordance with guidance

      - Any clinically important abnormalities in rhythm, conduction, or morphology of
      resting EKG, e.g., complete left bundle branch block, third degree heart block,
      second degree heart block, PR interval > 250 msec.

   - Patients with a prior or concurrent malignancy whose natural history or treatment has
   the potential to interfere with the safety or efficacy assessment of the
   investigational regimen for this trial

   - Concurrent Therapy

      - Patients who are receiving any other anticancer or investigational drug therapy

      - Patients receiving strong inducers of CYP3A4, strong inhibitors of CYP3A4 or
      CYP1A2 or CYP3A4 substrates with a narrow therapeutic index within 2 weeks of the
      first dose of savolitinib (3 weeks for St John's Wort). Strong inducers of CYP3A4
      and CYP3A4 substrates which have a narrow therapeutic range or CYP3A4 sensitive
      substrates should not be used during the trial or used with caution. Because the
      lists of these agents are constantly changing, it is important to regularly
      consult a frequently-updated medical reference. Patient drug information handout
      and wallet card should be provided to patients

      - Prior or current treatment with a MET inhibitor (e.g., foretinib, crizotinib,
      cabozantinib, or onartuzumab)

   - Patient is currently receiving any of the following herbal preparations or medications
   and cannot be discontinued 1 week (7 days) prior to enrollment (3 weeks for St. John's
   wort). These herbal medications include, but are not limited to: cannabis products,
   St. John's wort, kava, ephedra (ma huang), gingko biloba, dehydroepiandrosterone
   (DHEA), yohimbe, saw palmetto, and ginseng

   - Patient has undergone major surgical procedure =< 28 days prior to beginning study
   drug or a minor surgical procedure =< 7 days prior to beginning study drug. No waiting
   is required following port-a-cath placement

   - Patients who in the opinion of the investigator are unwilling or unable to return for
   required follow-up visits or obtain follow-up studies required to assess toxicity to
   therapy or to adhere to drug administration plan, other study procedures, and study
   restrictions

   - Patients with a history of allergic reactions attributed to compounds of similar
   chemical or biologic composition

   - Prisoners will be excluded from this study