Abstract As a corollary to the Red Queen hypothesis, host–parasite coevolution has been hypothesized to maintain genetic variation in both species. Recent theoretical work, however, suggests that reciprocal natural selection alone is insufficient to maintain variation at individual loci. As highlighted by our brief review of the theoretical literature, models of host–parasite coevolution often vary along multiple axes (e.g. inclusion of ecological feedbacks or abiotic selection mosaics), complicating a comprehensive understanding of the effects of interacting evolutionary processes on diversity. Here we develop a series of comparable models to explore the effect of interactions between spatial structures and antagonistic coevolution on genetic diversity. Using a matching alleles model in finite populations connected by migration, we find that, in contrast to panmictic populations, coevolution in a spatially structured environment can maintain genetic variation relative to neutral expectations with migration alone. These results demonstrate that geographic structure is essential for understanding the effect of coevolution on biological diversity. Abstract Overview of the six matching alleles models considered and their main results for the maintenance of host genetic diversity. Bolded text in the top half of the figure indicates results in which coevolution maintained diversity, either transiently (relative to neutrality) or in the long term. The bottom half of the figure highlights model features, including host–parasite coevolution, spatial set-up and time scale. In the coevolutionary model, hosts and parasites undergo both extrinsic birth and death as well as death and subsequent birth resulting from successful infection. Geography is defined as one of three options: one patch, two patches with migration and island–mainland with migration. Time scale is either continuous or discrete, with models correspondingly specified as either Moran or Wright–Fisher models.