Ageing is an increase in mortality and/or decline in fertility with advancing age. Evolutionary theories predict that ageing will evolve in response to the pattern of externally imposed hazards to survival and fertility; a prediction confirmed in new empirical studies. Recent studies of large cohorts of experimental animals and of humans have revealed that mortality rates do not continue to accelerate at very advanced ages. It has been suggested that evolutionary theories cannot account for these mortality patterns; however, this challenge is more apparent than real. Heterogeneity between individuals can shape mortality trajectories for populations, and recent evolutionary theory can both account for such heterogeneity and accommodate late-age mortality patterns.