Time always leaves its mark, and our genome is no exception. Mutations in the genome of somatic cells were first hypothesized to be the cause of aging in the 1950s, shortly after the molecular structure of DNA had been described. Somatic mutation theories of aging are based on the fact that mutations in DNA as the ultimate template for all cellular functions are irreversible. However, it took until the 1990s to develop the methods to test if DNA mutations accumulate with age in different organs and tissues and estimate the severity of the problem. By now, numerous studies have documented the accumulation of somatic mutations with age in normal cells and tissues of mice, humans, and other animals, showing clock-like mutational signatures that provide information on the underlying causes of the mutations. In this review, we will first briefly discuss the recent advances in next-generation sequencing that now allow quantitative analysis of somatic mutations. Second, we will provide evidence that the mutation rate differs between cell types, with a focus on differences between germline and somatic mutation rate. Third, we will discuss somatic mutational signatures as measures of aging, environmental exposure, and activities of DNA repair processes. Fourth, we will explain the concept of clonally amplified somatic mutations, with a focus on clonal hematopoiesis. Fifth, we will briefly discuss somatic mutations in the transcriptome and in our other genome, i.e., the genome of mitochondria. We will end with a brief discussion of a possible causal contribution of somatic mutations to the aging process.