The subclass Teleostei Müller was erected in 1845 to contain all fishes possessing intermuscular bones (e.g., epineurals and epipleurals) and two arterial valves (in the conus arteriosus), and that are characterized also by the absence of muscles at the basal arteria (ventral aorta). Since these characters proved difficult for diagnosing fossils, the content of Teleostei was problematic from the start. These three characters are valid and uniquely derived, but the recognition of the taxon Teleostei sensu Müller has been ignored for most of the past 150 years, and the content of the group has changed numerous times. Additionally, a polyphyletic concept of Teleostei was the predominant idea for most of the last century. It was only during the 1970s that the monophyly of Teleostei was demonstrated. Although its monophyly is accepted, its content and phylogenetic relationships have been a subject of disagreement, with only some recent consensus between morphologists and molecular biologists. Understanding the history of Teleostei requires knowledge of its fossils forms. The monophyly of the total group Teleostei, which now includes Triassic pholidophorids, is supported by numerous synapomorphies, such as autosphenotic without small dermal component; unpaired vomer (in adults); complete ring of two sclerotic bones oriented anterior and posterior to orbit; and a hypural articulating with a few caudal rays—with further transformations in more advanced teleosts. Current evidence indicates that some Late Triassic taxa (†Pholidophoretes salvus and †Knerichthys bronni) from Europe represent the oldest known †pholidophorids, and the European genus †Prohalecites from the Ladinian/Carnian (Triassic; c. 240 Ma) boundary represents the oldest stem teleost. The synapomorphies now shared by living teleosts appeared stepwise more than 100 million years ago in the common ancestors of the sequential sisters of now living groups; they did not originate in the common ancestor of the three main living teleost clades (elopomorphs, and osteoglossomorphs plus clupeocephalans), and the analyses of character distribution reflects the gradual accumulation of features that now diagnose Recent teleosts. A list of characters supporting these hierarchical phylogenetic levels is provided.