The genus Aztekium contains three species of small globular cactus. Discovered in 1929 by F. Ritter, in Rayones, Nuevo León, Mexico, this genus was thought to be monotypic (with Aztekium ritteri) until a second species (Aztekium hintonii) was discovered by George S. Hinton, in Galeana, Nuevo León in 1991. A further species, Aztekium valdesii, was discovered in 2011 by M.A. Alvarado Vázquez in the Sierra Madre Oriental mountains of Nuevo León; the name was formally published in 2013, although as of September 2013 the name is not accepted by secondary sources such as The Plant List.