Multiple myeloma (MM) is a genetically complex disease that evolves from pre-malignant stages, such as monoclonal gammaopathy of undetermined significance and smouldering multiple myeloma, and progresses to symptomatic MM; this continuum provides a unique framework to study the sequential genomic evolution of MM. In the past 5 years, results from large-scale whole-exome sequencing studies have provided new insights into the clonal heterogeneity and evolution of the disease. Moreover, the recurrent co-occurrence of genomic events helps to dissect the genomic complexity underlying tumour progression. According to the primary genetic events involved in tumorigenesis, MM tumours are hierarchically subdivided into hyperdiploid and non-hyperdiploid subtypes; subsequently, secondary genetic events lead to tumour progression. In this Review, we describe the 'driver' gene alterations involved in the development and progression of MM, with a focus on the sequential acquisition of the main genomic aberrations. We also provide valuable insight into the clonal heterogeneity and clonal evolution of the disease, as well as into the therapeutic implications of a comprehensive understanding of the genomic complexity of MM.