Wine fermentation and innovation have focused mostly on Saccharomyces cerevisiae strains. However, recent studies have shown that other Saccharomyces species can also be involved in wine fermentation or are useful for wine bouquet, such as Saccharomyces uvarum and Saccharomyces paradoxus. Many interspecies hybrids have also been isolated from wine fermentation, such as S. cerevisiae × Saccharomyces kudriavzevii hybrids. In this study, we explored the genetic diversity and fermentation performance of Spanish S. kudriavzevii strains, which we compared to other S. kudriavzevii strains. Fermentations of red and white grape musts were performed, and the phenotypic differences between Spanish S. kudriavzevii strains under different temperature conditions were examined. An ANOVA analysis suggested striking similarity between strains for glycerol and ethanol production, although a high diversity of aromatic profiles among fermentations was found. The sources of these phenotypic differences are not well understood and require further investigation. Although the Spanish S. kudriavzevii strains showed desirable properties, particularly must fermentations, the quality of their wines was no better than those produced with a commercial S. cerevisiae. We suggest hybridization or directed evolution as methods to improve and innovate wine.