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The simplest population models for predators-prey interactions and epidemics of disease are based on the assumption that populations are homogeneously mixed. However, recent studies of measles epidemics have concluded that age-related heterogeneities have a profound dynamical effect and that homogeneous models cannot explain observed epidemics. I will show that, in fact, the aggregate behaviour of age-structured epidemic models is effectively equivalent to that of a homogeneous model with external forcing, and I will argue that seasonal variation in contact rates is the key determinant of the temporal pattern of measles epidemics. I will also discuss some new results concerning synchronization of population dynamics in different spatial locations, and the potential importance of synchronization in vaccination programs.