The directly transmitted viviparous gyrodactylids have high species richness but low morphological and biological diversity, and many species are recorded from only a single host. They therefore constitute a guild of species ideal for studies of the evolutionary significance of host specificity. The group has the widest host range of any monogenean family, being found on 19 orders of bony fish. However, individual species range from narrowly specific (71% of 402 described species recorded from a single host) to extremely catholic (Gyrodactylus alviga recorded from 16 hosts). Gyrodactylid-host interactions extend from 60 mya (G. lotae, G. lucii) down to 150 years (G. derjavini on Oncorhynchus mykiss). Co-evolution with the host is comparatively rare within the gyrodactylids, but host switching or ecological transfer is common, and has been facilitated by the mixing of fish strains that followed glaciation. In this review, we consider the factors responsible for gyrodactylid specificity patterns, using examples from our work on salmonid gyrodactylids including G. salaris, responsible for major epidemics on wild Atlantic salmon (Salmo salar) in Norway since 1975, and G. thymalli from grayling and G. derjavini from trout.G. salaris has a wide host range with highest population growth rates on Norwegian salmon strains. However, growth rates are variable on both host strains and species, because of the multitude of micro- and macro-environmental factors influencing parasite mortality and fecundity. A better predictor of performance is the proportion of fishes of a strain which are innately resistant to the parasite, a measure which is negatively correlated with the time to peak infection in a host strain. Population growth rate is also negatively correlated with age of infection; the initial rate, therefore, predicts best the suitability of a fish as host for G. salaris. The host response to gyrodactylids appears to be the same mechanism in all salmonids with innate resistance as one end of a spectrum, but influenced by stress and probably under polygenic control. Hybrid experiments show that performance of G. salaris on a host is heritable, and usually intermediate between that of the parents. This host response mechanism, coupled with the initial parasite population growth on a fish, determines the host specificity, i.e. whether the fish will be susceptible, a responder or innately resistant. The use of population growth rate parameters allows comparison of different hosts as a resource for a gyrodactylid. In the case of G. salaris, East Atlantic and Baltic strains of Atlantic salmon are core hosts, but other salmonids can physiologically sustain infections for considerable periods, and may be important in parasite dispersal and transmission. A further group of non-salmonid fishes are unable to sustain G. salaris reproduction, but can act as transport hosts.Population growth parameters are very labile to stressors and environmental factors, particularly temperature and salinity, and also other aspects of host ecology and water quality. These factors may also influence the spectrum of hosts that can be infected under particular conditions, and probably favoured ecological transfer of gyrodactylids between host species in periglacial conditions. G. salaris may still be undergoing post-glacial range expansion (aided by anthropogenic spread) as shown by the increase in the species range over the last 25 years. The origin of G. salaris, G. teuchis and G. thymalli is discussed in relation to glacial refugiums during the last ice age.