Progressively sophisticated understanding of cellular and molecular processes that contribute to age-related physical deterioration is being gained from ongoing research into cancer, chronic inflammatory syndromes and other serious disorders that increase with age. Particularly valuable insight has resulted from characterization of how senescent cells affect the tissues in which they form in ways that decrease an organism's overall viability. Increasingly, the underlying pathophysiology of ageing is recognized as a consequence of oxidative damage. This leads to hyperactivity of cell growth pathways, prominently including mTOR (mammalian target of rapamycin), that contribute to a build-up in cells of toxic aggregates such as progerin (a mutant nuclear cytoskeletal protein), lipofuscin and other cellular debris, triggering formation of senescent cellular phenotypes, which interact destructively with surrounding tissue. Indeed, senescent cell ablation dramatically inhibits physical deterioration in progeroid (age-accelerated) mice. This review explores ways in which oxidative stress creates ageing-associated cellular damage and triggers induction of the cell death/survival programs’ apoptosis, necrosis, autophagy and ‘necroapoptophagy’. The concept of ‘necroapoptophagy’ is presented here as a strategy for varying tissue oxidative stress intensity in ways that induce differential activation of death versus survival programs, resulting in enhanced and sustained representation of healthy functional cells. These strategies are discussed in the context of specialized mesenchymal stromal cells with the potential to synergize with telocytes in stabilizing engrafted progenitor cells, thereby extending periods of healthy life. Information and concepts are summarized in a hypothetical approach to suppressing whole-organism senescence, with methods drawn from emerging understandings of ageing, gained from Cnidarians (jellyfish, corals and anemones) that undergo a unique form of cellular regeneration, potentially conferring open-ended lifespans.