Cellular senescence is an established cellular stress response that acts primarily to prevent the proliferation of cells that experience potentially oncogenic stress. In recent years, it has become increasingly apparent that the senescence response is a complex phenotype, which has a variety of cell non-autonomous effects. The senescence-associated secretory phenotype, or SASP, entails the secretion of numerous cytokines, growth factors and proteases. The SASP can have beneficial or detrimental effects, depending on the physiological context. One recently described beneficial effect is to aid tissue repair. Among the detrimental effects, the SASP can disrupt normal tissue structures and function, and, ironically, can promote malignant phenotypes in nearby cells. These detrimental effects in many ways recapitulate the degenerative and hyperplastic pathologies that develop during aging. Because the SASP is largely a response to genomic or epigenomic damage, we suggest it may be a model for a cellular damage response that can propagate damage signals both within and among tissues. We propose that both the degenerative and hyperplastic diseases of aging may be fueled by such damage signals.