Potato (Solanum tuberosum L.) is the world’s most important non-cereal food crop, and the vast majority of commercially grown cultivars are highly heterozygous tetraploids. Advances in diploid hybrid breeding based on true seeds have the potential to revolutionize future potato breeding and production1,2,3,4. So far, relatively few studies have examined the genome evolution and diversity of wild and cultivated landrace potatoes, which limits the application of their diversity in potato breeding. Here we assemble 44 high-quality diploid potato genomes from 24 wild and 20 cultivated accessions that are representative of Solanum section Petota, the tuber-bearing clade, as well as 2 genomes from the neighbouring section, Etuberosum. Extensive discordance of phylogenomic relationships suggests the complexity of potato evolution. We find that the potato genome substantially expanded its repertoire of disease-resistance genes when compared with closely related seed-propagated solanaceous crops, indicative of the effect of tuber-based propagation strategies on the evolution of the potato genome. We discover a transcription factor that determines tuber identity and interacts with the mobile tuberization inductive signal SP6A. We also identify 561,433 high-confidence structural variants and construct a map of large inversions, which provides insights for improving inbred lines and precluding potential linkage drag, as exemplified by a 5.8-Mb inversion that is associated with carotenoid content in tubers. This study will accelerate hybrid potato breeding and enrich our understanding of the evolution and biology of potato as a global staple food crop.