I present a historical review of coevolutionary models for the evolutionary persistence of sexual reproduction. The focus is on the fate of obligately sexual populations facing competition with one or more obligately asexual clones. An early simulation model by Hamilton (Hamilton WD. 1980. Sex versus non-sex versus parasite. Oikos. 35:282-290.) suggested that parasites could be an important force in selecting against asexual clones, leading to the persistence of sex. This result was consistent with a number of independent verbal models generated from 1975-1983. Conversely, the models by May and Anderson (May RM, Anderson RM. 1983. Epidemiology and genetics in the coevolution of parasites and hosts. Proc R Soc Lond B Biol Sci. 219:281-313.), which included more epidemiological detail, suggested that parasites were an unlikely source of selection to favor sexual over asexual reproduction. Thus began an oscillation of opinion regarding the role of parasites in selection for sex. It would seem at present that some of the differences of opinion over time stemmed from the different ways that models were constructed, including whether the sexual population was in competition with a genetically diverse asexual population or a single clonal genotype. On theoretical grounds, parasite-mediated selection for sex seems more likely if the sexual population has options in genotypic space that are not available to the clones. Models that incorporate more ecological realism also seem more favorable to the parasite theory of sex.