Of the more than 65,000 living species of chordates, about half are bony fish of the class Osteichthyes. The world's largest and fastest animals, the blue whale and peregrine falcon respectively, are chordates, as are humans.t has also proved difficult to produce a detailed classification within the living chordates. Attempts to produce evolutionary  family trees  give results that differ from traditional classes because several of those classes are not monophyletic. As a result, vertebrate classification is in a state of flux.