Clones of non-transformed human cells are mortal, that is, the cells divide only a limited number of times before they approach a state of proliferative senescence. This state has long been regarded as a cellular model of organismal aging or as aging in vitro because of its close relationship to the aging process of the donor of the cells. The underlying molecular mechanisms of this particular aging process have only been recently understood and are reviewed in the present paper. Cell division is accompanied by progressive telomere shortening, which is due both to properties of the replicative apparatus (the "end-replication problem") and to oxidative damage to telomere DNA under conventional cell culture conditions. If shortening of telomeres reaches a certain critical level, it is recognized as DNA damage by the cell's "guardian of the genome", the tumor suppressor p53. Stabilization of p53 activates the well characterized cell cycle checkpoint at the G1/S phase boundary and blocks the cell cycle irreversibly. Two recent results prove that telomere shortening is in fact the trigger of the checkpoint control in cellular senescence: First, acceleration of telomere shortening by increased oxidative stress results in accelerated proliferative senescence. Second, stabilization of telomere length, typically by activation of telomere, appears to be a necessary prerequisite for the immortalization of cells. Proliferative senescence, therefore, should be understood as an important means to counteract genetic instability and cancer.