The evolutionary theory of ageing lies in a complicated intersection among evolutionary genetics, population ecology, and mathematical demography. It is impossible to form a coherent model of the evolution of senescence without taking account of overlapping generations, environmental stochasticity, and genetic pleiotropy and epistasis on a grand scale, in addition to the elements that are standard in mathematical models of evolution. This talk will outline some recent progress and major outstanding questions, including an account of a general framework developed with Steve Evans and Ken Wachter, for analysing mutation-selection equilibrium in contexts with large numbers of nearly neutral mutations.