Aging is characterized by a decrease in genome integrity, impaired organ maintenance, and an increased risk of cancer, which coincide with clonal dominance of expanded mutant stem and progenitor cell populations in aging tissues, such as the intestinal epithelium, the hematopoietic system, and the male germline. Here we discuss possible explanations for age-associated increases in the initiation and/or progression of mutant stem/progenitor clones and highlight the roles of stem cell quiescence, replication-associated DNA damage, telomere shortening, epigenetic alterations, and metabolic challenges as determinants of stem cell mutations and clonal dominance in aging.