Evolutionary history and early association with anthropogenic environments have made Saccharomyces cerevisiae the quintessential wine yeast. This species typically dominates any spontaneous wine fermentation and, until recently, virtually all commercially available wine starters belonged to this species. The Crabtree effect, and the ability to grow under fully anaerobic conditions, contribute decisively to their dominance in this environment. But not all strains of Saccharomyces cerevisiae are equally suitable as starter cultures. In this article, we review the physiological and genetic characteristics of S. cerevisiae wine strains, as well as the biotic and abiotic factors that have shaped them through evolution. Limited genetic diversity of this group of yeasts could be a constraint to solving the new challenges of oenology. However, research in this field has for many years been providing tools to increase this diversity, from genetic engineering and classical genetic tools to the inclusion of other yeast species in the catalogues of wine yeasts. On occasion, these less conventional species may contribute to the generation of interspecific hybrids with S. cerevisiae. Thus, our knowledge about wine strains of S. cerevisiae and other wine yeasts is constantly expanding. Over the last decades, wine yeast research has been a pillar for the modernisation of oenology, and we can be confident that yeast biotechnology will keep contributing to solving any challenges, such as climate change, that we may face in the future.