Technical Abstract: Solanum tuberosum, the cultivated potato of world commerce, is a primary food crop worldwide. Wild and cultivated potatoes form the germplasm base for international breeding efforts to improve potato in the face of variety of disease, environmental, and agronomic constraints. A series of national and international genebanks collect, characterize, and distribute germplasm to stimulate and aid potato improvement. Knowledge of potato taxonomy and evolution guides collecting efforts, genebank operations, and breeding. Past taxonomic treatments of wild and cultivated potato have differed tremendously among authors regarding both the number of species recognized and hypotheses of their interrelationships. In total, there are 494 basionyms of wild and 560 basionyms of cultivated taxa, including names not validly published. Recent classifications, however, recognize only about 100 wild species and four cultivated species. This paper compiles, for the first time, names of all cultivated potato species, many of which have appeared only in the Russian literature, places them in synonymy, and provides lectotype designations for all names validly published where possible. We also summarize the history of differing taxonomic concepts in cultivated potato, and keys and descriptions to the four cultivated species.