The conjugating algae, an almost exclusively freshwater and extraordinarily diverse group of streptophyte green algae, are referred to a class generally known as the Conjugatophyceae in Central Europe and the Zygnematophyceae elsewhere in the world. Conjugatophyceae is widely considered to be a descriptive name and Zygnematophyceae ('Zygnemophyceae' a typified name. However, both are typified names and Conjugatophyceae Engler ('Conjugatae') is the earlier name. Additionally, Zygnemophyceae Round is currently an invalid name and is validated here as Zygnematophyceae Round ex Guiry. The names of orders, families and genera for conjugating green algae are reviewed. For many years these algae were included in the 'Conjugatae', initially used as the equivalent of an order. The earliest use of the name Zygnematales appears to be by the American phycologist Charles Edwin Bessey (1845-1915), and it was he who first formally redistributed all conjugating algae from the 'Conjugatae' to the orders Zygnematales and the Desmidiales. The family Closteriaceae Bessey, currently encompassing Closterium and Spinoclosterium, is illegitimate as it was superfluous when first proposed, and its legitimization is herein proposed by nomenclatural conservation to facilitate use of the name The genus Debarya Wittrock, 1872 is shown to be illegitimate as it is a later homonym of Debarya Schulzer, 1866 (Ascomycota), and the substitute genus name Transeauina Guiry is proposed together with appropriate combinations for 13 species currently assigned to the genus Debarya Wittrock. The relationships between Mougeotia, Mougeotiopsis, Mougeotiella, and Transeauina require further resolution, as do many of the other genera referred to the Conjugatophyceae. Type species are designated for genera for which no types were formally selected previously. The number of currently described species of conjugating green algae in AlgaeBase is about 3,500, comprising about 10% of all algal species, with about one third of species referred to the Zygnematales and two-thirds to the Desmidiales. A corresponding 10% of all algal names at the species level and below have been applied to conjugating algae, although a large proportion of these are at the infraspecific level.