Interpretations of conodont anatomy and affinity continue to generate controversy. Fossilized soft-tissue evidence indicates that conodonts possessed eyes, extrinsic eye muscles, a notochord, myomeres, a differentiated tail with fin radials, possible otic capsules and possible branchial structures. Indirect evidence suggests a differentiated brain and cartilaginous head skeleton. The multi-component phosphatic tissue complexes of the conodont feeding apparatus cannot be compared to the amorphous apatite of extant agnathan otoliths. By limiting cladistic analysis to a restricted selection of these characters the hypothesis that conodonts are a sister group of the clade comprising extant hagfish, lampreys and gnathostomes can be supported. However, exhaustive analysis of a more complete character-set strongly supports the hypothesis that conodonts are more derived than hagfish. From a taxonomic perspective, these two hypotheses have no effect on how conodonts should be classified. Whether they are a stem group (the former hypothesis) or part of the crown group (the latter), conodonts are clearly part of the total group Vertebrata (=Craniata).