Craniates, one of the three subdivisions of chordates, have distinct skulls-including hagfish, which have no vertebrae. Michael J. Benton comments, craniates are characterized by their heads, just as chordates, or possibly all deuterostomes, are by their tails.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.