Understanding the evolution of individuals which live in a structured and fluctuating population is of central importance in mathematical population biology. Two types of structure are important. First individuals live in a particular spatial location and their rate of reproduction depends on where they are and who is living near them. Second, if we are to make inferences from genetic data then we must understand how genes evolve as they pass through different genetic backgrounds. In this lecture we introduce some popular models of structured populations and highlight the mathematical challenges that arise from trying to extend them to better reflect biological populations.