Telomere erosion is considered to be the main cause of the onset of replicative senescence. However, recent findings suggest that a senescent phenotype can be induced by a variety of other stimuli that act independently of telomeres. Moreover, telomere-dependent replicative senescence depends on the species of cell origin, in particular whether cells are of human or rodent origin. In addition, the tissue of origin may also dictate the pathway by which cells undergo replicative senescence. In this Review article, we categorize cellular senescence into two types, which for simplicity we term intrinsic or extrinsic senescence, focus on the differences between human and mouse cells, and discuss the roles of the p53 and pRb tumor suppressor pathways in cellular senescence.