Infectious diseases undergo evolutionary changes as they spread and persist in populations. Different diseases present substantially different evolutionary dynamics, with both large-scale changes that create different strains, or more incremental shifts within a strain. In this talk, we demonstrate how a general stochastic epidemic model can be used to explain different types of evolutionary dynamics for infectious diseases. We describe how parameter choices correspond to evolutionary processes, and how simple building blocks within the model can be combined into more complex evolutionary behaviours. We compare model outputs to observed phylogenetic data from a variety of infectious diseases, including influenza, dengue, and Ebola.