For decades, cytogenetic studies have demonstrated that somatically acquired structural rearrangements of the genome are a common feature of most classes of human cancer. However, the characteristics of these rearrangements at sequence-level resolution have thus far been subject to very limited description. One process that is dependent upon somatic genome rearrangement is gene amplification, a mechanism often exploited by cancer cells to increase copy number and hence expression of dominantly acting cancer genes. The mechanisms underlying gene amplification are complex but must involve chromosome breakage and rejoining. We sequenced 133 different genomic rearrangements identified within four cancer amplicons involving the frequently amplified cancer genes MYC, MYCN, and ERBB2. The observed architectures of rearrangement were diverse and highly distinctive, with evidence for sister chromatid breakage–fusion–bridge cycles, formation and reinsertion of double minutes, and the presence of bizarre clusters of small genomic fragments. There were characteristic features of sequences at the breakage–fusion junctions, indicating roles for nonhomologous end joining and homologous recombination-mediated repair mechanisms together with nontemplated DNA synthesis. Evidence was also found for sequence-dependent variation in susceptibility of the genome to somatic rearrangement. The results therefore provide insights into the DNA breakage and repair processes operative in somatic genome rearrangement and illustrate how the evolutionary histories of individual cancers can be reconstructed from large-scale cancer genome sequencing.