Cellular senescence is a state of irreversible cell cycle arrest that often emerges after tissue damage and in age‐related diseases. Through the production of a multicomponent secretory phenotype (SASP), senescent cells can impact the regeneration and function of tissues. However, the effects of senescent cells and their SASP are very heterogeneous and depend on the tissue environment and type as well as the duration of injury, the degree of persistence of senescent cells and the organism's age. While the transient presence of senescent cells is widely believed to be beneficial, recent data suggest that it is detrimental for tissue regeneration after acute damage. Furthermore, although senescent cell persistence is typically associated with the progression of age‐related chronic degenerative diseases, it now appears to be also necessary for correct tissue function in the elderly. Here, we discuss what is currently known about the roles of senescent cells and their SASP in tissue regeneration in ageing and age‐related diseases, highlighting their (negative and/or positive) contributions. We provide insight for future research, including the possibility of senolytic‐based therapies and cellular reprogramming, with aims ranging from enhancing tissue repair to extending a healthy lifespan.