; Gard. Dict. Abr., ed. 4: s. p. (1754) s. str.
Distribution: North and South America. The species circumscription is sometimes highly disputed.
= Cactodendron J.M.Bigelow; Pacif. Railr. Rep., Bot. 4(5, no. 3), Bot. [Whipple]: 102 (1856), nom. inval.
= Chaffeyopuntia Frič & Schelle ex Kreuz.; Verzeichnis Amer. Sukk. Rev. Syst. Kakteen 42 (1935)
= Clavarioidia Kreuz.; Verzeichnis Amer. Sukk. Rev. Syst. Kakteen 41 (1935), nomen
= Clavatopuntia Frič & Schelle; Verzeichnis Amer. Sukk. Rev. Syst. Kakteen, p. ? (1935), nom. inval.
= Ficindica St.-Lag.; Ann. Soc. Bot. Lyon 7: 70 (1880)
= Nopal M.Ocampo; nom. illeg.
= Nopalea Salm-Dyck; Cact. Hort. Dyck. [1849 ed.]: 63, 233 (1850)
= Parviopuntia Soulaire; nom. inval.
= Phyllarthus Neck. ex M.Gomez; Fl. Cuba [M.Gómez & Roig] 119 (1914)
= Platyopuntia (Engelm.) Frič & Schelle ex Kreuz.; Verzeichnis Amer. Sukk. Rev. Syst. Kakteen 42 (1935)
= Plutonopuntia P.V.Heath; Calyx 6(2): 41 (1999), nom. nov.
= Subulatopuntia Frič & Schelle; Verzeichnis Amer. Sukk. Rev. Syst. Kakteen 10 (1935)
= Terecaulis F.Berge
= Tunas Lunell; Amer. Midl. Naturalist 4: 479 (1916)