Many features of aging result from the incapacity of cells to adapt to stress conditions. When damage accumulates irreversibly, mitotic cells from renewable tissues rely on either of two mechanisms to avoid replication. They can permanently arrest the cell cycle (cellular senescence) or trigger cell death programs. Apoptosis (self-killing) is the best-described form of programmed cell death, but autophagy (self-eating), which is a lysosomal degradation pathway essential for homeostasis, reportedly contributes to cell death as well. Unlike mitotic cells, postmitotic cells like neurons or cardiomyocytes cannot become senescent since they are already terminally differentiated. The fate of these cells entirely depends on their ability to cope with stress. Autophagy then operates as a major homeostatic mechanism to eliminate damaged organelles, long-lived or aberrant proteins and superfluous portions of the cytoplasm. In this mini-review, we briefly summarize the molecular networks that allow damaged cells either to adapt to stress or to engage in programmed-cell-death pathways.