Non-Saccharomyces are important during wine fermentation once they influence wine composition. In the early stages of wine fermentation, and together with indigenous or commercial strains of Saccharomyces cerevisiae, non-Saccharomyces are able to transform grape-must sugars into ethanol, CO2, and other important secondary metabolites. A better understanding of yeast biochemistry will allow the selection of yeast strains that have defined specific influences on fermentation efficiency, wine quality, and the production of human health-promoting compounds. Yeast metabolism produces compounds derived from tryptophan, melatonin, and serotonin, which are found in fermented beverages, such as wine and beer. Melatonin is a neurohormone secreted from the pineal gland and has a wide-ranging regulatory and neuroprotective role, while serotonin, as well as being a precursor of melatonin synthesis, is also a neurotransmitter. This review summarizes the importance of some conventional and nonconventional yeast strains’ alcoholic fermentations, especially in the production of metabolites that promote human health and thus, attract consumers attention towards fermented beverages. A brief reference is also made on fermented beverages containing probiotics, namely kombucha, also known as kombucha tea, and its interesting microorganism’s symbiotic relationships named SCOBY.