AbstractSpatial structure has dramatic effects on the demography and the evolution of species. A large variety of theoretical models have attempted to understand how local dispersal may shape the coevolution of interacting species such as host–parasite interactions. The lack of a unifying framework is a serious impediment for anyone willing to understand current theory. Here, we review previous theoretical studies in the light of a single epidemiological model that allows us to explore the effects of both host and parasite migration rates on the evolution and coevolution of various life‐history traits. We discuss the impact of local dispersal on parasite virulence, various host defence strategies and local adaptation. Our analysis shows that evolutionary and coevolutionary outcomes crucially depend on the details of the host–parasite life cycle and on which life‐history trait is involved in the interaction. We also discuss experimental studies that support the effects of spatial structure on the evolution of host–parasite interactions. This review highlights major similarities between some theoretical results, but it also reveals an important gap between evolutionary and coevolutionary models. We discuss possible ways to bridge this gap within a more unified framework that would reconcile spatial epidemiology, evolution and coevolution.