Wine represents a complex matrix in which microbial interactions can strongly impact the quality of the final product. Numerous studies have focused on optimizing microbial approaches for addressing new challenges to enhance quality, typicity, and food safety. However, few studies have investigated yeasts of different genera as resources for obtaining wines with new, specific traits. Currently, based on the continuous changes in consumer demand, yeast selection within conventionalSaccharomyces cerevisiaeand unconventional non-Saccharomycesyeasts represents a suitable opportunity. Wine fermentation driven by indigenous yeasts, in the various stages, has achieved promising results in producing wines with desired characteristics, such as a reduced content of ethanol, SO2, and toxins, as well as an increased aromatic complexity. Therefore, the increasing interest in organic, biodynamic, natural, or clean wine represents a new challenge for the wine sector. This review aims at exploring the main features of different oenological yeasts to obtain wines reflecting the needs of current consumers in a sustainability context, providing an overview, and pointing out the role of microorganisms as valuable sources and biological approaches to explore potential and future research opportunities.