Multiple myeloma is an incurable plasma cell malignancy with a complex and incompletely understood molecular pathogenesis. Here we use whole-exome sequencing, copy-number profiling and cytogenetics to analyse 84 myeloma samples. Most cases have a complex subclonal structure and show clusters of subclonal variants, including subclonal driver mutations. Serial sampling reveals diverse patterns of clonal evolution, including linear evolution, differential clonal response and branching evolution. Diverse processes contribute to the mutational repertoire, including kataegis and somatic hypermutation, and their relative contribution changes over time. We find heterogeneity of mutational spectrum across samples, with few recurrent genes. We identify new candidate genes, including truncations of SP140, LTB, ROBO1 and clustered missense mutations in EGR1. The myeloma genome is heterogeneous across the cohort, and exhibits diversity in clonal admixture and in dynamics of evolution, which may impact prognostic stratification, therapeutic approaches and assessment of disease response to treatment.