Multiple myeloma (MM) has a heterogeneous genome, evolving through both pre-clinical and post-diagnosis phases. Here, using sequences from 67 MM genomes serially collected from 30 patients together with public datasets, we establish a hierarchy of driver lesions. Point mutations, structural variants and copy number aberrations define at least 7 genomic subgroups of MM, each with distinct sets of co-operating driver mutations. Complex structural events are major drivers of MM, including chromothripsis, chromoplexy and a replication-based mechanism of templated insertions: these typically occur early. Hyperdiploidy also occurs early, with individual chromosomes often gained in more than one chronological epoch of MM evolution, showing a preferred order of acquisition. Positively selected point mutations frequently occur in later phases of disease development, as do structural variants involving MYC. Thus, initiating driver events of MM, drawn from a limited repertoire of structural and numerical chromosomal changes, shape preferred trajectories of subsequent evolution. MFAG (n.17658).