There is general consensus that the living elasmobranchs comprise a monophyletic taxon. There is evidence that, among tetraphyllidean tapeworms, the approximately 201 hooked species (Onchobothriidae) may also comprise a monophyletic group. Determinations of host specificity are contingent upon correct specific identifications. Since 1960, over 200 new elasmobranch species and over 100 new onchobothriid species have been described. Some confidence can be placed in host and parasite identifications of recent studies, but specific identifications provided in older literature in many cases are suspect. There is some consensus among published works on the phylogenetic relationships among elasmobranchs. Phylogenetic relationships among onchobothriids remain largely unresolved. Elasmobranchs have been poorly sampled for onchobothriids; records exist for approximately 20% of the 911 species and approximately 44% of the 170 elasmobranch genera. Onchobothriids are remarkably host specific, exhibiting essentially oioxenous specificity for their definitive hosts. Multiple onchobothriid species commonly parasitise the same host species; in some cases these are congeners, in other cases these are members of two different onchobothriid genera. There is substantial incongruence between available host and parasite phylogenies. For example, Acanthobothrium is by far the most ubiquitous onchobothriid genus, parasitising almost all orders of elasmobranchs known to host onchobothriids, yet, there is no evidence of major clades of Acanthobothrium corresponding to postulated major subgroupings of elasmobranchs (e.g. Galea and Squalea or sharks and rays). Potamotrygonocestus appears to be among the most basal onchobothriid groups, yet it parasitises one of the most derived elasmobranch groups (the freshwater stingray genus Potamotrygon). It appears that congeners parasitising the same host species are not necessarily each other's closest relatives. At this point the preliminary and limited available data suggest that, at least in this system, strict host specificity is not necessarily indicative of strict co-evolution. This study was extremely limited by the lack of available robust phylogenies for onchobothriids and elasmobranchs.