Potato (Solanum tuberosum L.), mankind's third most consumed food crop, originated as an interspecific hybrid in the Andean highlands. More than 100 species closely related to potato exist throughout Central and South America. Potato was introduced to Europe, Asia, and North America in the 16th and 17th centuries, but most cultivars were destroyed by late blight epidemics in the mid‐19th century. Late blight resistance genes from the wild relative Solanum demissum Lindl. were subsequently introduced into cultivated potato. Thus, a precedent for the use of wild relatives in potato genetic improvement was established a century ago. Intensive efforts have been made to collect and maintain wild relatives of potato in public germplasm repositories. Genetic diversity in these species is high, and most are sexually compatible with cultivated potato. Perhaps more than any other vegetable crop, potato can benefit from the introgression of genes for valuable traits from wild relatives. However, a century of breeding has realized that potential on only a few notable occasions. Important examples include improved processing quality and resistance to viruses and nematodes. Substantial barriers prevent the facile incorporation of genetic material from wild relatives into potato cultivars. Overcoming these barriers may require an expansion of germplasm collections to include well‐characterized individuals as a complement to population‐based accessions. To be most useful for potato improvement, individual wild species plants will need to be cataloged by allelic composition, haplotype, biochemical properties, and physiological responses to stress. Effectively using the genetic diversity in wild relatives is likely to rely heavily on alternative methods of potato breeding, augmenting reassortment, and selection at the tetraploid level with diploid breeding and genetic modification using biotechnology.