The concept of the force of natural selection was developed to explain the evolution of ageing. After ageing, however, comes a period in which mortality rates plateau and some individual organisms could, in theory, live forever. This late–life immortality has no presently agreed upon explanation. Two main theories have been offered. The first is heterogeneity within ageing cohorts, such that only extremely robust individuals survive ageing. This theory can be tested by comparisons of more and less robust cohorts. It can also be tested by fitting survival data to its models. The second theory is that late–life plateaus in mortality reflect the inevitable late–life plateau in the force of natural selection. This theory can be tested by changing the force of natural selection in evolving laboratory populations, particularly the age at which the force plateaus. This area of research has great potential for elucidating the overall structure of life–history evolution, particularly the interrelationship between the three life–history phases of development, ageing and immortality.