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 , in Galeana, Nuevo León in 1991. A further possible species, Aztekium valdezii, was described in 2011, but is considered to be a synonym of A. ritteri.