The Iridaceae Family was named and described by Antoine Laurent de Jussieu in Genera Plantarum in 1789.
Plants of the World Online lists 70 accepted genera in this family commonly referred to as the Iris family. It contains many very well-known genera with bulbs, corms, or rhizomes. I am not ready to go through that many genera and add up all the accepted species.
The first paragraph in the Wikipedia article says there are 66 accepted genera with a total of 2,244 species. Farther down it says up to 80 genera have been recognized with a total of around 1,500 species.
The 2013 version of The Plant List (no longer maintained) names 80 accepted genera plus a number of unresolved genera. It included a total of 2,456 species, 6,121 synonyms, and 327 unresolved names (species and infraspecific names).
Plants of the World Online was initiated by and is maintained by Kew but they are still uploading data. The Plant List was a cooperative effort mainly between Kew and the Missouri Botanical Garden but it is no longer maintained or up to date. The APG I-IV systems are continually restructuring the world of plants, so information changes periodically and you can’t blame anyone for having different statistics.
For more information about this family of plants, please click on the links below. The links take you directly to the information about the family.