The multiple myeloma (MM) genome is heterogeneous and evolves through preclinical and post-diagnosis phases. Here we report a catalog and hierarchy of driver lesions using sequences from 67 MM genomes serially collected from 30 patients together with public exome datasets. Bayesian clustering defines at least 7 genomic subgroups with distinct sets of co-operating events. Focusing on whole genome sequencing data, complex structural events emerge as major drivers, including chromothripsis and a novel replication-based mechanism of templated insertions, which typically occur early. Hyperdiploidy also occurs early, with individual trisomies often acquired in different chronological windows during evolution, and with a preferred order of acquisition. Conversely, positively selected point mutations, whole genome duplication and chromoplexy events occur in later disease phases. Thus, initiating driver events, drawn from a limited repertoire of structural and numerical chromosomal changes, shape preferred trajectories of evolution that are biologically relevant but heterogeneous across patients.