Ray-finned fishes (Actinopterygii) dominate modern aquatic ecosystems and are represented by over 32000 extant species. The vast majority of living actinopterygians are teleosts; their success is often attributed to a genome duplication event or morphological novelties. The remainder are ‘living fossils’ belonging to a few depauperate lineages with long-retained ecomorphologies: Polypteriformes (bichirs), Holostei (bowfin and gar) and Chondrostei (paddlefish and sturgeon). Despite over a century of systematic work, the circumstances surrounding the origins of these clades, as well as their basic interrelationships and diagnoses, have been largely mired in uncertainty. Here, I review the systematics and characteristics of these major ray-finned fish clades, and the early fossil record of Actinopterygii, in order to gauge the sources of doubt. Recent relaxed molecular clock studies have pushed the origins of actinopterygian crown clades to the mid-late Palaeozoic [Silurian–Carboniferous; 420 to 298 million years ago (Ma)], despite a diagnostic body fossil record extending only to the later Mesozoic (251 to 66 Ma). This disjunct, recently termed the ‘Teleost Gap’ (although it affects all crown lineages), is based partly on calibrations from potential Palaeozoic stem-taxa and thus has been attributed to poor fossil sampling. Actinopterygian fossils of appropriate ages are usually abundant and well preserved, yet long-term neglect of this record in both taxonomic and systematic studies has exacerbated the gaps and obscured potential synapomorphies. At the moment, it is possible that later Palaeozoic-age teleost, holostean, chondrostean and/or polypteriform crown taxa sit unrecognized in museum drawers. However, it is equally likely that the ‘Teleost Gap’ is an artifact of incorrect attributions to extant lineages, overwriting both a post-Palaeozoic crown actinopterygian radiation and the ecomorphological diversity of stem-taxa.