The analysis of model systems has broadened our understanding of telomere-related aging processes. Telomerase-deficient mouse models have demonstrated that telomere dysfunction impairs tissue renewal capacity and shortens lifespan. Telomere shortening limits cell proliferation by activating checkpoints that induce replicative senescence or apoptosis. These checkpoints protect against an accumulation of genomically instable cells and cancer initiation. However, the induction of these checkpoints can also limit organ homeostasis, regeneration, and survival during aging and in the context of diseases. The decline in tissue regeneration in response to telomere shortening has been related to impairments in stem cell function. Telomere dysfunction impairs stem cell function by activation of cell-intrinsic checkpoints and by the induction of alterations in the micro- and macro-environment of stem cells. In this review, we discuss the current knowledge about the impact of telomere shortening on disease stages induced by replicative cell aging as indicated by studies on telomerase model systems.