1. Invasions can impact on parasite communities through both the introduction of exotic parasite species and effects of invading hosts on native parasite dynamics. However, our understanding of the factors that influence the invasive process and mediate impacts on native hosts and parasites is limited. 2. Using models of host—parasite dynamics as a framework, we explore how both the probability of spread for an exotic parasite and impacts of introduced species on native parasite dynamics depend on key parameters related to rates of encounter, transmission, mortality and recovery. We examine how invasions may interact with the diverse range of underlying biological mechanisms that can affect these rates. We specifically highlight the potential role of interactions between parasites, which has largely been ignored. 3. For introduced parasites, high abundance of competent hosts and vectors within native communities can greatly facilitate spread. Introduced host species can cause amplification or dilution effects for native parasite dynamics, with the direction and magnitude of the effect determined by how the invasion influences the competency and abundance or relative abundance of the host community (community capacity). 4. Invasions by exotic parasites and changes to endemic parasite dynamics following invasions may reflect numerical and functional processes in multihost single-parasite systems (e.g. influence of host and vector community structure on encounter rates). However, as co-infection can influence factors such as susceptibility and infection length, effects may also be mediated by within-host interactions between parasites. The ultimate effect of an invasion will depend on the community-wide summed direct and indirect impacts. 5. Future studies should aim to further elucidate the key processes influencing disease dynamics in multihost (and multivector) communities, thereby informing predictions of how invasive host and parasite species and changes in biodiversity will influence disease risk. Theoretical studies should incorporate host interspecific competition and relax assumptions regarding the relationship between intra- and interspecific contact rates and density. Empirical and experimental studies should not only quantify the relative importance of host (and vector) density and diversity, but also consider other community interactions such as those between parasites.