A vertebral column consisting of a persistent notochord and ossified arcocentra is the primitive condition for Gnathostomata; it still persists in primitive actinopterygians and sarcopterygians. Advanced actinopterygians and sarcopterygians develop numerous types of centra that include, among others, the presence of holocentrum, chordacentrum, and autocentrum. The chordacentrum, a mineralization or calcification of the fibrous sheath of the notochord, is only found in actinopterygians, whereas an autocentrum is a synapomorphy of teleosts above †Leptolepis coryphaenoides. The chordacentrum, formed by migration of cartilaginous cells from the arches into the fibrous sheath of the notochord and usually covered by a thin calcification, is a unique feature of chondrichthyans. The actinopterygian chordacentrum and the chondrichthyan chordacentrum are not homologous. The postcaudal cartilaginous centrum is only known in postcaudal vertebrae of living dipnoans. The holocentrum is present in certain fossil dipnoans and actinopterygians, where it has been independently acquired. It is formed by proliferation of cartilage cells around the elastica externa of the notochord. These cells later ossify, forming a compact centrum. A vertebral column formed by a persistent notochord without vertebral centra is the primitive pattern for all vertebrates. The formation of centra, which is not homologous among vertebrate groups, is acquired independently in some lineages of placoderms, most advanced actinopterygians, and some dipnoans and rhipidistians. Several series of structures are associated with the vertebral column such as the supraneurals, interhaemals, radials, and ribs. In living dipnoans median neural spine, ‘supraneural’, and dorsal radial result from growth and distal differentiation of one median cartilage into two or three median bones during ontogeny. The median neural spine articulates with the neural arch and fuses with it in the caudal vertebrae early in ontogeny. Two bones differentiate in the anterior abdominal vertebrae, i.e., the proximal neural spine and the distal ‘supraneural.’ Three bones differentiate in front of the dorsal fin, i.e., the proximal neural spine, the middle ‘supraneural,’ and the distal radial; the same pattern is observed in front of the anal fin (the proximal haemal spine, the middle interhaemal, and the distal radial). Considering that the three dorsal (and also the three ventral) bones originate from growth of only one cartilage, they cannot be serial homologs of the neural spines, or ‘supraneural.’ They are linear homologs of the median neural cartilage in living dipnoans. The development of these elements differs within osteichthyans from sarcopterygians to actinopterygians, in which the neural spine originates as a continuation of the basidorsal arcualia and in which the supraneural and radial originate from independent cartilages that appear at different times during early ontogeny. The ribs of living dipnoans are unique in that they are not articulated with parapophyses, like in primitive fossil dipnoans, but a remnant of the ventral arcuale surrounded by a small arcocentrum remains at its base. A true caudal fin is absent in living dipnoans. The postcaudal cartilages extend to the caudal tip of the body separating dorsal and ventral rays (or the camptotrichia). Actinotrichia are present in young dipnoans. They are also known in extant actinistians and actinopterygians. They probably represent the primitive state for teleostomes. In contrast, the camptotrichia are unique for extant dipnoans (and probably Carboniferous and younger dipnoans). Lepidotrichia apparently developed many times among osteichthyans.