Apparent competition is indirect competition between two or more victim species that share a natural enemy, caused by that enemy's numerical response. We review empirical examples of apparent competition in phytophagous insect hosts attacked by polyphagous parasitoids and develop models of apparent competition in host-parasitoid systems. Apparent competition is particularly likely in insect assemblages because parasitoids can limit their hosts to levels at which resource competition is unimportant. A consideration of both equilibrium and nonequilibrium models in which polyphagous parasitoids impose significant mortality on their hosts suggests that the most common outcome is the exclusion of all but one host species, which generates dynamic monophagy (i.e., a single host species persisting with a potentially polyphagous parasitoid). A crisp criterion for dominance in apparent competition is that the winning host supports the highest parasitoid density. We conclude that it is difficult for alternative hosts to coexist when the sole regulatory factor is a shared parasitoid. Yet in nature, coexisting hosts frequently do share parasitoids. We examine several mechanisms promoting host coexistence, including donor-controlled parasitoid dynamics, additional sources of host density dependence (e.g., resource limitation), spatial and temporal refuges, trophic web structure, and labile parasitoid behavior. Elucidating the mechanisms permitting the coexistence of host species confronted by effective polyphagous parasitoids deserves more attention from experimental field ecologists.