Potato is the most important non-cereal crop worldwide, and, yet, genetic gains in potato have been traditionally delayed by the crop’s biology, mostly the genetic heterozygosity of autotetraploid cultivars and the intricacies of the reproductive system. Novel site-directed genetic modification techniques provide opportunities for designing climate-smart cultivars, but they also pose new possibilities (and challenges) for breeding potato. As potato species show a remarkable reproductive diversity, and their ovules have a propensity to develop apomixis-like phenotypes, tinkering with reproductive genes in potato is opening new frontiers in potato breeding. Developing diploid varieties instead of tetraploid ones has been proposed as an alternative way to fill the gap in genetic gain, that is being achieved by using gene-edited self-compatible genotypes and inbred lines to exploit hybrid seed technology. In a similar way, modulating the formation of unreduced gametes and synthesizing apomixis in diploid or tetraploid potatoes may help to reinforce the transition to a diploid hybrid crop or enhance introgression schemes and fix highly heterozygous genotypes in tetraploid varieties. In any case, the induction of apomixis-like phenotypes will shorten the time and costs of developing new varieties by allowing the multi-generational propagation through true seeds. In this review, we summarize the current knowledge on potato reproductive phenotypes and underlying genes, discuss the advantages and disadvantages of using potato’s natural variability to modulate reproductive steps during seed formation, and consider strategies to synthesize apomixis. However, before we can fully modulate the reproductive phenotypes, we need to understand the genetic basis of such diversity. Finally, we visualize an active, central role for genebanks in this endeavor by phenotyping properly genotyped genebank accessions and new introductions to provide scientists and breeders with reliable data and resources for developing innovations to exploit market opportunities.