Wine is a processed beverage that offers high nutritional and health benefits. It is produced from grape must, which undergoes fermentation by yeasts (and sometimes lactic acid bacteria) to create a product that is highly appreciated by consumers worldwide. However, if only one type of yeast, specifically Saccharomyces cerevisiae, were used in the fermentation process, the resulting wine would lack aroma and flavor and may be rejected by consumers. To produce wine with a desirable taste and aroma, non-Saccharomyces yeasts are necessary. These yeasts contribute volatile aromatic compounds that significantly impact the wine’s final taste. They promote the release of primary aromatic compounds through a sequential hydrolysis mechanism involving several glycosidases unique to these yeasts. This review will discuss the unique characteristics of these yeasts (Schizosaccharomyces pombe, Pichia kluyveri, Torulaspora delbrueckii, Wickerhamomyces anomalus, Metschnikowia pulcherrima, Hanseniaspora vineae, Lachancea thermotolerans, Candida stellata, and others) and their impact on wine fermentations and co-fermentations. Their existence and the metabolites they produce enhance the complexity of wine flavor, resulting in a more enjoyable drinking experience.