The cancer genome is moulded by the dual processes of somatic mutation and selection. Homozygous deletions in cancer genomes occur over recessive cancer genes, where they can confer selective growth advantage, and over fragile sites, where they are thought to reflect an increased local rate of DNA breakage. However, most homozygous deletions in cancer genomes are unexplained. Here we identified 2,428 somatic homozygous deletions in 746 cancer cell lines. These overlie 11% of protein-coding genes that, therefore, are not mandatory for survival of human cells. We derived structural signatures that distinguish between homozygous deletions over recessive cancer genes and fragile sites. Application to clusters of unexplained homozygous deletions suggests that many are in regions of inherent fragility, whereas a small subset overlies recessive cancer genes. The results illustrate how structural signatures can be used to distinguish between the influences of mutation and selection in cancer genomes. The extensive copy number, genotyping, sequence and expression data available for this large series of publicly available cancer cell lines renders them informative reagents for future studies of cancer biology and drug discovery.