Analysis of maximum depth of occurrence of 11 952 marine fish species shows a global decrease in species number (N) with depth (x; m): log10N = −0·000422x + 3·610000 (r2 = 0·948). The rate of decrease is close to global estimates for change in pelagic and benthic biomass with depth (−0·000430), indicating that species richness of fishes may be limited by food energy availability in the deep sea. The slopes for the Classes Myxini (−0·000488) and Actinopterygii (−0·000413) follow this trend but Chondrichthyes decrease more rapidly (−0·000731) implying deficiency in ability to colonize the deep sea. Maximum depths attained are 2743, 4156 and 8370 m for Myxini, Chondrichthyes and Actinopterygii, respectively. Endemic species occur in abundance at 7–7800 m depth in hadal trenches but appear to be absent from the deepest parts of the oceans, >9000 m deep. There have been six global oceanic anoxic events (OAE) since the origin of the major fish taxa in the Devonian c. 400 million years ago (mya). Colonization of the deep sea has taken place largely since the most recent OAE in the Cretaceous 94 mya when the Atlantic Ocean opened up. Patterns of global oceanic circulation oxygenating the deep ocean basins became established coinciding with a period of teleost diversification and appearance of the Acanthopterygii. Within the Actinopterygii, there is a trend for greater invasion of the deep sea by the lower taxa in accordance with the Andriashev paradigm. Here, 31 deep‐sea families of Actinopterygii were identified with mean maximum depth >1000 m and with >10 species. Those with most of their constituent species living shallower than 1000 m are proposed as invasive, with extinctions in the deep being continuously balanced by export of species from shallow seas. Specialized families with most species deeper than 1000 m are termed deep‐sea endemics in this study; these appear to persist in the deep by virtue of global distribution enabling recovery from regional extinctions. Deep‐sea invasive families such as Ophidiidae and Liparidae make the greatest contribution to fish fauna at depths >6000 m.