Most cells cannot divide indefinitely due to a process termed cellular or replicative senescence. Replicative senescence appears to be a fundamental feature of somatic cells, with the exception of most tumour cells and possibly certain stem cells. How do cells sense the number of divisions they have completed? Although it has not yet been critically tested, the telomere shortening hypothesis is currently perhaps the best explanation for a cell division ‘counting’ mechanism. Why do cells irreversibly cease proliferation after completing a finite number of divisions? It is now known that replicative senescence alters the expression of a few crucial growth-regulatory genes. It is not known how these changes in growth-regulatory gene expression are related to telomere shortening in higher eukaryotes. However, lower eukaryotes have provided several plausible mechanisms. Finally, what are the physiological consequences of replicative senescence? Several lines of evidence suggest that, at least in human cells, replicative senescence is a powerful tumour suppressive mechanism. There is also indirect evidence that replicative senescence contributes to ageing. Taken together, current findings suggest that, at least in mammals, replicative senescence may have evolved to curtail tumorigenesis, but may also have the unselected effect of contributing to age-related pathologies, including cancer.