Stem cell senescence may play a central role in both aging and age-related pathologies, being associated with a functional impairment of both homeostasis and the regenerative properties of tissues. The possibility to interfere with this detrimental phenomenon requires a careful elucidation of the mechanisms that initiate and maintain this cellular response. In this review, we will discuss the hypothesis that cellular senescence could be considered the biological memory of the action of different types of stressors on the organism, leading to a complex phenotype that includes both intrinsic (e.g., gene expression, chromatin organization, and cell metabolism) and extrinsic (e.g., secretome) changes. Finally, it will be shown that cell senescence blunts the regenerative ability of human cardiac stem cells and that the pharmacological inhibition of this detrimental cell process restores the functional properties of primitive cells in vivo.