Cultivated potatoes have been classified as species under the International Code of Botanical Nomenclature (ICBN) and as cultivar-groups under the International Code of Nomenclature of Cultivated Plants (ICNCP); both classifications are still widely used. This study examines morphological support for the classification of landrace populations of cultivated potatoes, using representatives of all seven species and most subspecies as outlined in the latest taxonomic treatment. These taxa are S. ajanhuiri, S. chaucha, S. curtilobum, S. juzepczukii, S. phureja subsp. phureja, S. stenotomum subsp. stenotomum, S. stenotomum subsp. goniocalyx, S. tuberosum subsp. andigenum, and S. tuberosum subsp. tuberosum. The results show some phenetic support for S. ajanhuiri, S. chaucha, S. curtilobum, S. juzepczukii, and S. tuberosum subsp. tuberosum, but little support for the other taxa. Most morphological support is by using a suite of characters, all of which are shared with other taxa (polythetic support). These results, combined with their likely hybrid origins, multiple origins, evolutionary dynamics of continuing hybridization, and our classification philosophy, leads us to recognize all landrace populations of cultivated potatoes as a single species, S. tuberosum, with the eight cultivar-groups: Ajanhuiri Group, Andigenum Group, Chaucha Group, Chilotanum Group, Curtilobum Group, Juzepczukii Group, Phureja Group, and Stenotomum Group. We defer classification of modern cultivars, traditionally classified in Tuberosum Group, to a later study.