Ageing is driven by the inexorable and stochastic accumulation of molecular damage that eventually compromises cellular function. While this process is fundamentally haphazard and uncontrollable, ageing is broadly influenced by genetic and extrinsic factors. It is becoming increasingly apparent that most such interventions interface with stress response mechanisms, suggesting that longevity is intimately related to the ability of the organism to effectively cope with both intrinsic and extrinsic stress. Key determinants of this capacity are the molecular pathways that underlie age-related changes in the effectiveness of the response to stress. General and cargo-specific autophagy emerges as an integral part of cellular and systemic stress responses. We find that mitophagy, a selective type of autophagy targeting mitochondria, and nucleophagy, the selective autophagic recycling of nuclear material are important determinants of germline immortality and somatic ageing, under conditions of stress. These homeostatic mechanisms are vital in long-lived neuronal cells, where they mediate damage removal during ageing to prevent neurodegeneration.