Cancer cells evolve from normal cells by somatic mutations and natural selection. Comparing the evolution of cancer cells and that of organisms can elucidate the genetic basis of cancer. Here we analyse somatic mutations in >400 cancer genomes. We find that the frequency of somatic single-nucleotide variations increases with replication time during the S phase much more drastically than germ-line single-nucleotide variations and somatic large-scale structural alterations, including amplifications and deletions. The ratio of nonsynonymous to synonymous single-nucleotide variations is higher for cancer cells than for germ-line cells, suggesting weaker purifying selection against somatic mutations. Among genes with recurrent mutations only cancer driver genes show evidence of strong positive selection, and late-replicating regions are depleted of cancer driver genes, although enriched for recurrently mutated genes. These observations show that replication timing has a prominent role in shaping the single-nucleotide variation landscape of cancer cells.