Our review of the taxonomy of Australia’s endemic Calyptorhynchinae black cockatoos based on morphology, ecology, biology, vocalisations, distributions, and genetic studies concluded that they constitute two genera; those with red subterminal tail bands in the genus Calyptorhynchus Desmarest, 1826 and those with white or yellow subterminal tail bands in the genus Zanda Mathews, 1913. We also concluded that the genus Calyptorhynchus is made up of six monotypic species: Northern Red-tailed Cockatoo C. banksii Latham, 1790; South-eastern Red-tailed Cockatoo C. graptogyne Schodde, Saunders and Homberger, 1988; Forest Red-tailed Cockatoo C. naso Gould, 1837; Inland Red-tailed Cockatoo C. samueli Mathews, 1917; Western Red-tailed Cockatoo C. escondidus Ewart, Joseph and Schodde, 2020; and Glossy Cockatoo C. lathami Temminck, 1807. Formerly, the five red-tailed taxa were regarded as subspecies and the Glossy Cockatoo consisted of three subspecies. In addition, we concluded that the genus Zanda is made up of five monotypic species: two with white subterminal tail bands, Baudin’s Cockatoo Z. baudinii Lear, 1832 and Carnaby’s Cockatoo Z. latirostris Carnaby, 1948; and three with yellow subterminal tail bands, Eastern Yellow-tailed Cockatoo Z. funerea Shaw, 1794, Western Yellow-tailed Cockatoo Z. whiteae Mathews, 1912, and Tasmanian Yellow-tailed Cockatoo Z. xanthanota Gould, 1838. Formerly, the three yellow-tailed taxa were regarded as subspecies. As all cockatoos with coloured subterminal tail bands are black, we recommend deleting the word black from their common names.