It is generally believed that the first organisms did not age, and that aging thus evolved at some point in the history of life. When and why this transition occurred is a fundamental question in evolutionary biology. Recent reports of aging in bacteria suggest that aging predates the emergence of eukaryotes and originated in simple unicellular organisms. Here we use simple models to study why such organisms would evolve aging. These models show that the differentiation between an aging parent and a rejuvenated offspring readily evolves as a strategy to cope with damage that accumulates due to vital activities. We use measurements of the age-specific performance of individual bacteria to test the assumptions of the model, and find evidence that they are fulfilled. The mechanism that leads to aging is expected to operate in a wide range of organisms, suggesting that aging evolved early and repeatedly in the history of life. Aging might thus be a more fundamental aspect of cellular organisms than assumed so far.