Melanoma of the skin is a common cancer only in Europeans, whereas it arises in internal body surfaces (mucosal sites) and on the hands and feet (acral sites) in people throughout the world. Here we report analysis of whole-genome sequences from cutaneous, acral and mucosal subtypes of melanoma. The heavily mutated landscape of coding and non-coding mutations in cutaneous melanoma resolved novel signatures of mutagenesis attributable to ultraviolet radiation. However, acral and mucosal melanomas were dominated by structural changes and mutation signatures of unknown aetiology, not previously identified in melanoma. The number of genes affected by recurrent mutations disrupting non-coding sequences was similar to that affected by recurrent mutations to coding sequences. Significantly mutated genes included BRAF, CDKN2A, NRAS and TP53 in cutaneous melanoma, BRAF, NRAS and NF1 in acral melanoma and SF3B1 in mucosal melanoma. Mutations affecting the TERT promoter were the most frequent of all; however, neither they nor ATRX mutations, which correlate with alternative telomere lengthening, were associated with greater telomere length. Most melanomas had potentially actionable mutations, most in components of the mitogen-activated protein kinase and phosphoinositol kinase pathways. The whole-genome mutation landscape of melanoma reveals diverse carcinogenic processes across its subtypes, some unrelated to sun exposure, and extends potential involvement of the non-coding genome in its pathogenesis.