The family, Iridaceae Juss., was named and described as such by Antoine Laurent de Jussieu in Genera Plantarum in 1789.
On 2-1-21 when I last updated this page, 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 page says it was updated in January 2021 but it says the same thing it did in 2018.
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.