A survey of the great mass of papers which have appeared since 1920 dealing with the ostracoderms shows that many matters of structure and interpretation are still in doubt, despite the existence of many exquisitely preserved fossils of members of the group, and detailed descriptions of them. Critical consideration of published accounts and of new materials show: That Stensio's account of the structure of the head skeleton of Cephalaspis is correct. That the gills of Cephalaspis were more probably pouches of adult cyclostome pattern than of the type suggested by Stensio. That the series of gill pouches includes two (one innervated by the profundus and one by the trigeminus) anterior to the hyoidean or spiracular gill cleft. The heterostracan Anglaspis appears to have had gill pouches, and shows nasal openings lying on the roof of the mouth cavity. The joint naso-hypophysial opening of cyclostomes on the top of the head is formed, as Goodrich showed, by the development of an upper lip as part of a larval feeding mechanism, so that cephalaspids, anaspids, lampreys and hagfishes are brigaded together with the probability that in their ancestry there were animals with an ammocoete larva. The cephalaspid pectoral fins are shown to be neomorphs, not homologous with those of craniates. The so-called 'electric fields' of Cephalaspis are newly interpreted as special sense organs allowing pressure waves incident on the head to be conveyed along liquid-filled canals to the ear. The character of the body cavity of Cephalaspis is such that it is probable that its heart already showed a characteristic cyclostome asymmetry.