Chordates (phylum Chordata) include the vertebrates, together with several closely related invertebrates. They are united by having, at some stage in their life, a notochord, a hollow dorsal nerve cord, pharyngeal slits and a tail extending past the anus.
The phylum Chordata is broken down into three subphyla: Urochordata, Cephalochordata, and Vertebrata. Urochordate larvae have a notochord and a nerve cord but they are lost in adulthood. Cephalochordates have a notochord and a nerve cord but no vertebrae. In vertebrates, the notochord has been replaced by a bony vertebral column.
The extant groups of chordates are related as shown in the phylogenetic tree, below. They do not match up very well with the traditional groups, and as a result vertebrate classification is in a state of flux, although their relationships are very well understood.
The distant ancestor of teleostomes that lived in sea of Latest Ordovician, whatever it was, its autapomorphies were enough to eventually out-compete every other vertebrate group.
The Acanthodii were successful teleostomes, but they went extinct by Permian Period, leaving the Teleostomi's daughter clade, Osteichthyes, to remain the dominant clade and continued to evolve.
Characters: Mouth terminal; braincase deep and narrow; braincase shows ventral fissure, otic-occipital fissure; separate ant and post nostrils; large bone operculum and/or branchiostegal rays.
The Devonian is frequently called, with ample reason, the "Age of Fishes." The stage for this explosion of aquatic vertebrates was undoubtedly set in the Silurian, perhaps due to the duplication of ancestral hox genes.
The recent discovery of the Guildayichthyiforms adds substantial clarity to the picture and may change our idea of the Actinopterygii considerably.