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Gene-for-gene (GFG) and matching-allele (MA) models are qualitatively different paradigms for describing the outcome of genetic interactions between hosts and pathogens. The GFG paradigm was largely built on the foundations of Flor’s early work on the flax-flax rust interaction and is based on the concept of genetic recognition leading to incompatible disease outcomes, typical of host immune recognition. In contrast, the MA model is based on the assumption that genetic recognition leads to compatible interactions, which can result when pathogens require specific host factors to cause infection. Results from classical MA and GFG models have led to important predictions regarding various coevolutionary phenomena, including the role of fitness costs associated with resistance and infectivity, the distribution of resistance genes in wild populations, patterns of local adaptation and the evolution and maintenance of sexual reproduction. Empirical evidence (which we review briefly here), particularly from recent molecular advances in understanding of the mechanisms that determine the outcome of host-pathogen encounters, suggests considerable variation in specific details of the functioning of interactions between hosts and pathogens, which may contain elements of both models. In this regard, GFG and MA scenarios likely represent endpoints of a continuum of potentially more complex interactions that occur in nature. Increasingly, this has been recognized in theoretical studies of coevolutionary processes in plant host-pathogen and animal host-parasite associations (e.g. departures from strict GFG/MA assumptions, diploid genetics, multi-step infection processes). However, few studies have explored how different genetic assumptions about host resistance and pathogen infectivity might impact on disease epidemiology or pathogen persistence within and among populations. Here, we use spatially explicit simulations of the basic MA and GFG scenarios to highlight qualitative differences between these scenarios with regard to patterns of disease and impacts on host demography. Given that such impacts drive evolutionary trajectories, future theoretical advances that aim to capture more complex genetic scenarios should explicitly address the interaction between epidemiology and different models of host-pathogen interaction genetics.