Hamilton and Zuk (1982) suggested that females could continuously base their choice of mates on heritable resistance to parasites, as generated in a process of coadaptational cycles of hosts and their parasites and advertized in terms of individual differences in plumage features or displays of the chosen sex. This hypothesis was based on three assumptions: (1) the full expression of secondary sexual traits of individual hosts is dependent on their overall health and vigour; (2) hosts are coevolving with their parasites, thereby continuously generating heritable resistance to parasites; and (3) parasites have negative effects on host viability. Given these assumptions one may then make the following intra- and interspecific predictions: (1) females will obtain mates with few or no parasites by choosing males with fully expressed sexual ornaments, (2) males with inferior ornaments will be less desirable partners and therefore take longer to become mated, (3) assortative mating occurs with respect to parasite loads, (4) females which mate with males with poorly developed secondary sexual characters will copulate outside their pair bond with males showing more fully expressed ornaments, and (5) in species especially vulnerable to parasite invasions, sexual selection will lead to more extreme development of health-certifying traits, allowing females to more accurately assess the parasite load of a male. Here I shall evaluate the empirical evidence for these assumptions and predictions and discuss alternative hypotheses advanced, in order to explain the importance of parasites for the sexual selection theory. An open question not yet studied satisfactorily is whether, and how often, coadaptational cycles exist, and, if they exist, how they should affect mate choice.