Wine fermentation is a biochemical process carried out by a microbial consortium already present in the vineyard, including different species of fungi and bacteria that are in an ecological relationship with each other, so that their sequential growth causes the transformation of grape must into wine. Among the fungi, the unicellular ones, yeasts, stand out, including Saccharomyces cerevisiae, which is mainly responsible for driving alcoholic fermentation, as do other species present from the beginning of fermentation, known as non-Saccharomyces yeasts. These yeasts were previously considered harmful and undesirable; however, their role has recently been re-evaluated, mainly because they can provide products and effects that are of great value in achieving a quality final product. In this review, we discuss the role of non-Saccharomyces wine yeasts, firstly with regard to their biocontrol activity both on the grapes and during the vinification process and secondly with regard to their ability to produce enzymes, especially depolymerising ones. In this context, the possible biotechnological applications of these non-Saccharomyces yeasts to improve the health and quality of grape and wine production are addressed.