All chordates are deuterostomes, meaning that the anus develops before the mouth in early embryonic stages, and all share typical chordate features, though it might not be obvious to look at some of them. The classification within each of the aove groups have changed little in the past few decades with the exception of the Myxini (hagfish). It used to be thought that hagfish were vertebrates, but in fact these "fish" have no backbone at all. However, they do have a cranium (skull), and so a new group has been named, the Craniata, to include those chordates that have a cranium.
Some zoologists would put the Urochordata closer to the Echinodermata, instead of within the Chordata proper. A few paleontologists would place the Echinodermata closer to the Chordata or even within the Chordata, based on some unusual Paleozoic fossil echinoderms (the Homalozoa) that have been interpreted as having a tail and pharyngeal slits. We plan to update this exhibit as more information becomes available.
Visit the Tree of Life for more detailed information on chordate systematics.