Age is the main risk factor for the prevalent diseases of developed countries: cancer, cardiovascular disease and neurodegeneration. The ageing process is deleterious for fitness, but can nonetheless evolve as a consequence of the declining force of natural selection at later ages, attributable to extrinsic hazards to survival: ageing can then occur as a side-effect of accumulation of mutations that lower fitness at later ages, or of natural selection in favour of mutations that increase fitness of the young but at the cost of a higher subsequent rate of ageing. Once thought of as an inexorable, complex and lineage-specific process of accumulation of damage, ageing has turned out to be influenced by mechanisms that show strong evolutionary conservation. Lowered activity of the nutrient-sensing insulin/insulin-like growth factor/Target of Rapamycin signalling network can extend healthy lifespan in yeast, multicellular invertebrates, mice and, possibly, humans. Mitochondrial activity can also promote ageing, while genome maintenance and autophagy can protect against it. We discuss the relationship between evolutionarily conserved mechanisms of ageing and disease, and the associated scientific challenges and opportunities.