Wild and cultivated potatoes (Solanum section Petota) present challenges to taxonomists arising from lack of clearly defined morphological character differences among many species, phenotypic plasticity, a range of ploidy levels from diploid to hexaploid, and hybrid speciation and introgression. Taxonomic treatments of the group have differed greatly regarding numbers of species and hypotheses of their interrelationships at the series level. Recent morphological phenetic studies and molecular studies have confirmed the general lack of clearly defined species, have shown the need to use a number of character states with overlapping ranges for species delimitation (polythetic support), and have suggested the need for the reduction of species in section Petota. Molecular studies have sometimes confirmed hypotheses of hybridization and sometimes have failed to support them. Molecular studies have suggested the need for a reconsideration of the traditionally held series concepts. Currently, section Petota contains 196 wild species and a single cultivated species, Solanum tuberosum, with eight landrace cultivar groups, exclusive of the modern cultivars that are not yet classified into cultivar groups. The number of wild species likely will decrease with future study. These points are here illustrated by (1) a discussion of published species level studies in Solanum series Longipedicellata, the Solanum brevicaule complex, and the cultivated landrace populations of potatoes; (2) reinvestigations of hybridization in S. chacoense, S. raphanifolium and S. xrechei; and (3) studies of ingroup and outgroup relationships of section Petota.