There is considerable current interest in the role that parasites can play in biological invasions. This review looks at the fate of parasites during a biological invasion and at their impact on native and invasive hosts, and asks whether parasites can mediate invasion success. An introduced species may lose its parasites as a result of the introduction and such release from its natural enemies may be an important factor determining invasion success. In addition, an introduced species may acquire parasites from its new environment or it may introduce novel parasites to hosts in the new range. As a result of local adaptation, parasites tend to have a differential effect on native versus invading hosts. The relative impact on the fitness of natives and invaders can be important for the outcome of an invasion and may, for example, reverse the pattern of competitive dominance seen in uninfected hosts. Parasites may mediate invasion success through their effect on host fitness and thus on host population growth and stability. Furthermore, by modifying host-host interactions (including competition and predation), parasites can be important factors that determine the success of an invasion and its impact on the recipient community.