Abstract A notochord is characteristic of developing chordates (which comprise amphioxus, tunicates and vertebrates), and, more arguably, is also found in some other animals. Although notochords have been well reviewed from a developmental genetic point of view, there has heretofore been no adequate survey of the dozen or so scenarios accounting for their evolutionary origin. Advances in molecular phylogenetics and developmental genetics have, on the one hand, failed to support many of these ideas (although, it is not impossible that some of these rejects may yet, at least in part, return to favor). On the other hand, current molecular approaches have actually stimulated the revival of two of the old proposals: first that the notochord is a novelty that arose in the chordates, and second that it is derived from a homologous structure, the axochord, that was present in annelid-like ancestors. In the long term, choosing whether the notochord is a chordate novelty or a legacy from an ancient annelid (or perhaps an evolutionary derivative from precursors yet to be proposed) will probably require descriptions of gene regulatory networks involved in the development of notochords and notochord-like structures in a wide spectrum of animals. For now, one-way forward will be studies of all aspects of the biology of enteropneust hemichordates, a group widely thought to be the key to understanding the evolutionary origin of the chordates.