Inclusion Criteria:

          -  Written informed consent - a signed informed consent and/or assent (as age
             appropriate) will be obtained according to institutional guidelines.

          -  Male or female >=12 months and <18 years of age at the time of signing the informed
             consent form.

          -  Recurrent disease, refractory disease, or progressive disease after having received at
             least one standard therapy for their disease. Note: Subjects with metastatic (and
             surgically unresectable) melanoma can be enrolled for first-line treatment; Melanoma
             subjects with CNS involvement may be enrolled.

          -  At least one evaluable lesion.

          -  BRAF V600 mutation-positive tumor as confirmed in a Clinical Laboratory Improvement
             Amendments (CLIA)-approved laboratory or equivalent (the local BRAF testing may be
             subject to subsequent verification by centralized testing; centralized testing can
             confirm V600E and V600K mutations only).

          -  Performance score of >=50% according to the Karnofsky/Lansky performance status scale
             (subjects with a performance status of <=50% can be enrolled if the subject's
             confinement to bed and inability to carry out activities is due solely to
             cancer-related pain, as assessed by the investigator).

          -  Females of child-bearing potential (with negative serum pregnancy test within 7 days
             prior to the first dose of study medication) must be willing to practice acceptable
             methods of birth control .

          -  Sexually active males, who do not agree to abstinence, must be willing to use a condom
             during intercourse while taking the study drug, and for 16 weeks after stopping
             treatment and should not father a child in this period.

          -  Must have adequate organ function as defined by the following values: Adequate bone
             marrow function defined as-absolute neutrophil count (ANC) >=1000/ microliter (µL),
             hemoglobin >=8.0 grams (g)/ deciliter (dL) (may receive red blood cell transfusions),
             platelets >=75,000/µL (transfusion independent, defined as not receiving platelet
             transfusions within a 7 day period prior to enrollment).

          -  Adequate renal and metabolic function defined as: calculated glomerular filtration
             rate (eGFR) (Schwartz formula), or radioisotope GFR >=90 milliliters/minutes
             (mL/min)/1.73 meter square (m^2); or a serum creatinine within the institutional
             reference range upper limit of normal (for age/gender, if available).

          -  Adequate liver function defined as: bilirubin (sum of conjugated + unconjugated) <=1.5
             x upper limit of normal (ULN) for age, aspartate aminotransaminase (AST) and alanine
             transaminase (ALT) <=2.5 x ULN; AST/ALT may be <5 x ULN at baseline if disease under
             treatment involves the liver (requires radiographic confirmation of liver
             involvement).

          -  Adequate cardiac function defined as: left ventricular ejection fraction (LVEF) of
             either >=50% by ECHO or greater than institutional lower limit of normal (LLN) by
             echocardiogram (ECHO) (while not receiving medications for cardiac function),
             corrected QT using Bazett's (QTcB) interval <450 milliseconds (msecs).

        Exclusion Criteria:

          -  Part 2 ONLY: Previous treatment with dabrafenib, another RAF inhibitor, or a
             mitogen-activated protein kinase (MEK) inhibitor (exception: prior treatment with
             sorafenib is permitted).

          -  Malignancy OTHER than the BRAF mutant malignancy under study.

          -  Had chemotherapy or radiotherapy within 3 weeks (or 6 weeks for nitrosoureas or
             mitomycin C) prior to administration of the first dose of study treatment.

          -  The subject has received an investigational product within the following time period
             prior to the first dosing day in the current study: 28 days or 5 half-lives or twice
             the duration of the biological effect of the investigational product (whichever is
             warranted by the data).

          -  History of another malignancy. Exception: (a) Subjects who have been successfully
             treated and are disease-free for 3 years, (b) a history of completely resected
             non-melanoma skin cancer, (c) successfully treated in situ carcinoma, (d) CLL in
             stable remission are eligible.

          -  Current use of a prohibited medication or herbal preparation or requires any of these
             medications during the study.

          -  Unresolved toxicity greater than National Cancer Institute Common Terminology Criteria
             for Adverse Events (NCI CTCAE) v4.0 Grade 2 or higher from previous anti-cancer
             therapy, including major surgery except those that in the opinion of the investigator
             are not clinically relevant given the known safety/toxicity profile of dabrafenib
             (e.g., alopecia and/or peripheral neuropathy related to platinum or vinca alkaloid
             based chemotherapy).

          -  Has leukaemia.

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to dabrafenib and its excipients.

          -  Autologous or allogeneic stem cell transplant within 3 months prior to enrolment
             [NOTE: subjects with evidence of active graph versus host disease are excluded].

          -  History of myocardial infarction, severe or unstable angina, peripheral vascular
             disease or familial QTc prolongation.

          -  Subjects with abnormal cardiac valve morphology (>=grade 2) documented by
             echocardiogram (NOTE: subjects with grade 1 abnormalities [i.e., mild
             regurgitation/stenosis] can be entered on study).

          -  Subjects with moderate valvular thickening.

          -  Known, uncontrolled cardiac arrhythmias (except sinus arrhythmia) within the past 24
             weeks

          -  Uncontrolled medical conditions (e.g., diabetes mellitus, hypertension, liver disease
             or uncontrolled infection), psychological, familial, sociological, or geographical
             conditions that do not permit compliance with the protocol; or unwillingness or
             inability to follow the procedures required in the protocol.

          -  Presence of active GI disease or other condition (e.g., small bowel or large bowel
             resection) that will interfere significantly with the absorption of drugs.

          -  Hepatitis B Virus, or Hepatitis C Virus infection (subjects with laboratory evidence
             of Hepatitis B Virus clearance may be enrolled).

          -  Pregnant females as determined by positive human chorionic gonadotropin (hCG) test at
             screening or prior to dosing.

          -  Lactating females who are actively breast feeding.