Genome instability is a fundamentally important component of aging in all eukaryotes. How age-related genome instability occurs remains unclear. The free radical theory of aging posits oxidative damage to DNA and other cellular constituents as a primary determinant of aging. More recent versions of this theory predict that mitochondria are a major source of reactive oxygen species (ROS) that cause oxidative damage. Although substantial support for the free radical theory exists, the results of some tests of this theory have been contradictory or inconclusive. Enhanced growth signaling also has been implicated in aging. Many efforts to understand the effects of growth signaling on aging have focused on inhibition of oxidative stress responses that impact oxidative damage. However, recent experiments in the model organism Saccharomyces cerevisiae (budding yeast) and in higher eukaryotes suggest that growth signaling also impacts aging and/or age-related diseases--including cancer and neurodegeneration--by inducing DNA replication stress, which causes DNA damage. Replication stress, which has not been broadly considered as a factor in aging, may be enhanced by ROS that signal growth. In this article, we review evidence that points to DNA replication stress and replication stress-induced genome instability as important factors in aging.