Several species of Agave L. (Agavaceae / Asparagaceae) have intricate nomenclatural histories, given that material imported into Europe from their New World habitats took several years, if not decades to flower, resulting in hasty and cryptic descriptions often being based on vegetative material only. Furthermore, multiple authors sometimes, but not always, used the same binomials to refer to plants known in cultivation, making it important to clarify and establish correct author citations to determine which species are referred to. In this paper we clarify the use of the well-known names Agave applanata Hort. ex K.Koch, A. verschaffeltii Lem. ex Jacobi and A. ghiesbreghtii Hort. ex Jacobi. In addition, notes are provided on 12 further species names that K. Koch established and, where appropriate, furnished by him with descriptive statements in an often overlooked paper that he published in 1862.