Grus, by L. Reichenbach, in Avium systema naturale. Das natürliche System der Vögel (Dresden and Leipzig: Expedition der vollständigsten Naturgeschichte, 1849), pl. 21. All subsequent illustrations refer to this plate.

Gruidae as a family name for Cranes was first used by Nicholas Aylward Vigors in a paper read to the Linnean Society of London, 3 December 1823, published as ‘Observations on the Natural Affinities That Connect the Orders and Families of Birds’, Transactions of the Linnean Society of London 14, pt 3 (1825): 413 (mentioned), 488 (descr.).

Four genera of extant cranes are being distinguished: Balearica, Leucogeranus, Antigone and Grus.

Two additional genera are being embedded within Grus by the IOC, but might well become split following Carey Krajewski, Justin T. Sipiorski and Frank E. Anderson, ‘Complete Mitochondrial Genome Sequences and the Phylogeny of Cranes (Gruiformes: Gruidae)’, Auk 127, no. 2 (2010): 440–452:

This leaves the following 15 species.