Inclusion Criteria:

          -  Patients with histologically confirmed diagnosis of glioma (WHO Grades I-IV) will be
             eligible. Patient tumors must test positive for the BRAFV600E mutation at University
             of California, San Francisco (UCSF) Molecular Pathology central laboratory. If
             mutation cannot be confirmed from a prior test and archival tumor is not available to
             confirm presence of BRAFV600E mutation, patients must have tumor biopsy to collect
             tumor sample for mutation confirmation.

          -  Patient must be less than 18 years of age at registration for the safety study.
             Patients must be < 25 years of age for Phase 0 and Efficacy Cohorts.

          -  Patients with neurological deficits should have deficits that are stable for a minimum
             of 1 week prior to registration.

          -  Patients must be able to swallow tablets (or applesauce, if part of bioavailability
             "crushed" six patient cohort).

          -  Patient must have magnetic resonance (MR) imaging performed within two weeks of first
             dose of drug.

          -  Karnofsky Performance Scale (KPS for > 16 yrs of age) or Lansky Performance Score(LPS
             for ≤ 16 years of age) ≥ 60 assessed within two weeks prior to registration.

          -  The patient must have failed at least one prior therapy besides surgery- radiation or
             chemotherapy (either cytotoxic or biologic agent)- prior to study registration.
             Patients must have fully recovered from the acute toxic effects of all prior
             chemotherapy, immunotherapy, or radiotherapy prior to entering this study.

          -  Myelosuppressive chemotherapy: Patients must have received their last dose of known
             myelosuppressive anticancer chemotherapy at least three weeks prior to study
             registration or at least six weeks if nitrosourea.

          -  Biologic agent: Patient must have recovered from any toxicity potentially related to
             the agent and received their last dose of the biologic agent ≥ 7 days prior to study
             registration.

          -  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. The duration of this interval should be discussed with the
             study chair.

          -  For biologic agents that have a prolonged half-life, the appropriate interval since
             last treatment should be discussed with the study chair prior to registration.

          -  Monoclonal antibody treatment: At least three half-lives must have elapsed prior to
             registration. Such patients should be discussed with the study chair prior to
             registration.

          -  Radiation: Patients must have:

          -  Had their last fraction of local irradiation to primary tumor ≥12 weeks prior to
             registration; investigators are reminded to review potentially eligible cases to avoid
             confusion with pseudo-progression.

          -  Had their last fraction of craniospinal irradiation or total body irradiation > 12
             weeks prior to registration

          -  Bone Marrow Transplant: Patient must be:

          -  ≥ 6 months since allogeneic bone marrow transplant prior to registration

          -  ≥ 3 months since autologous bone marrow/stem cell prior to registration

          -  Corticosteroids: Patients who are receiving dexamethasone must be on a stable or
             decreasing dose for at least 1 week prior to registration.

          -  Growth factors: Off all colony forming growth factor(s) for at least 1 week prior to
             registration (filgrastim, sargramostim, erythropoietin) and at least 2 weeks for long-
             acting formulations.

          -  Organ Function: Documented within 14 days of registration and within 7 days of the
             start of treatment.

          -  Adequate bone marrow function:

          -  Absolute neutrophil count ≥ 1000/μl (unsupported)

          -  Platelets ≥ 75,000/μl (unsupported)

          -  Hemoglobin ≥ 8 g/dL (may be supported)

          -  Adequate hepatic function:

          -  Total bilirubin < 1.5 times upper limit of normal for age

          -  serum glutamate pyruvate transaminase (SGPT)/serum glutamate oxaloacetate transaminase
             (SGOT) (ALT/AST) ≤ 2.5 times institutional upper limit of normal for age

          -  Adequate renal function:

          -  Creatinine clearance or Radioisotope glomerular filtration rate (GFR) ≥ 70
             ml/min/1.73m2 or a serum creatinine based on age as follows: Less than or equal to 5
             years of age= Maximum Serum Creatinine (mg/dL)of 0.8; Older than 5 but 10 years or
             younger= Maximum Serum Creatinine (mg/dL)of 1.0; Older than 10 but 15 years or
             younger= Maximum Serum Creatinine (mg/dL)of 1.2; Older than 15 years= Maximum Serum
             Creatinine (mg/dL) of 1.5

          -  Electrolytes:

          -  Sodium: ≥ 130 and ≤ 145 mmol/L

          -  Potassium: 3.4- 4.8 mmol/L

          -  Calcium: ≥ 7 mg/dL

          -  Magnesium: ≥ 0.7 mmol/L

          -  Nutrition:

          -  Albumin ≥ 3 g/dL

          -  Cardiac:

          -  Corrected QT (QTc) interval <450 msec on EKG.

          -  Female patients of childbearing potential must not be pregnant or breast-feeding.
             Female patients of childbearing potential must have a negative serum or urine
             pregnancy test. The effects of Vemurafenib on the developing human fetus are unknown.
             For this reason, women of child-bearing potential and men must agree to use adequate
             contraception: (hormonal or barrier method of birth control; abstinence) prior to
             study entry and for the duration of study participation, and for four weeks after
             dosing with vemurafenib ceases. Women must refrain from donating eggs during this same
             period. Should a woman become pregnant or suspect she is pregnant while she or her
             partner is participating in this study, she should inform her treating physician
             immediately. Men treated or enrolled on this protocol must also agree to use adequate
             contraception prior to the study, for the duration of study participation, and 4 weeks
             after completion of study drug administration.

          -  All skin lesions suspicious for keratoacanthomas/cutaneous squamous cell carcinoma
             (cSCC) found at baseline dermatology visit must have been excised.

          -  Signed informed consent according to institutional guidelines must be obtained.

        Specific inclusion criteria for Pre-Surgical Cohort:

          -  Patients under 25 years of age will be eligible for the pre-surgical cohort. Patients
             between 18-25 years of age will be treated at the adult FDA-approved dose of 960 mg
             BID and can be enrolled immediately. Patients less than 18 years of age will be
             enrolled and treated at the pediatric MTD once it is defined in the Safety Cohort.

          -  Surgical patients must have tumor that needs to be removed/debulked and is accessible
             for the neurosurgeon. Need for surgery must be such that the patient can take drug for
             10 days before surgery.

        Specific inclusion criteria for Expansion cohort:

        • Expansion cohort will be open if tissue drug levels in the Pre-Surgical cohort meet
        criteria (Tumor tissue drug concentration is greater than 50 nM). Patients under 25 years
        of age will be eligible for the expansion cohort. Patients between 18 and 25 years of age
        will take adult dose of 960 mg BID. Patients less than 18 years of age will take the MTD
        defined in the safety cohort.

        Exclusion Criteria:

          -  Patients with any clinically significant unrelated systemic illness (serious
             infections or significant cardiac, pulmonary, hepatic or other organ dysfunction) that
             will likely interfere with the study procedures or results.

          -  All patients with known clinical diagnosis of Neurofibromatosis Type 1 are excluded.

          -  Patients receiving any other anticancer or investigational drug therapy.

          -  Patients with uncontrolled seizures are not eligible for the study.

          -  Previous BRAF inhibitor use such as vemurafenib, GSK2118436 or sorafenib.

          -  Patients with QTc interval >450 msecs or other factors that increase the risk of
             QTprolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history
             of long QT interval syndrome) including heart failure that meets New York Heart
             Association(NYHA) class III and IV definitions are excluded.

          -  Required use of a concomitant medication that can prolong the QT interval. A
             comprehensive list of agents with the potential to cause QTc prolongation can be found
             at http://www.azcert.org/medical-pros/drug-lists/browse-drug-list.cfm?alpha=A

          -  Patients with inability to return for follow-up visits or obtain follow-up studies
             required to assess toxicity to therapy.

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to vemurafenib.

          -  Negative result of BRAFV600E screening test performed at UCSF.