Spontaneously occurring mutations accumulate in somatic cells throughout a person’s lifetime. The majority of these mutations do not have a noticeable effect, but some can alter key cellular functions. Early somatic mutations can cause developmental disorders, whereas the progressive accumulation of mutations throughout life can lead to cancer and contribute to aging. Genome sequencing has revolutionized our understanding of somatic mutation in cancer, providing a detailed view of the mutational processes and genes that drive cancer. Yet, fundamental gaps remain in our knowledge of how normal cells evolve into cancer cells. We briefly summarize a number of the lessons learned over 5 years of cancer genome sequencing and discuss their implications for our understanding of cancer progression and aging.