A Study to Determine Safety, Tolerability and Pharmacokinetics of Oral Dabrafenib In Children and Adolescent Subjects

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.