Georgia is recognized as one of the world’s earliest known centers of grape cultivation and wine production, as well as the home of 525 indigenous grape varieties. Phenolic compounds are a diverse group of secondary metabolites which are present in both grapes and wine, with the phenolic derivatives determining the organoleptic properties and the antioxidant activity of the resulting wines. Remarkably, the content and composition of phenolic compounds in wine are mainly influenced by the grape variety and the winemaking method. In this context, herein we review the present knowledge on the phenolic composition of the most common Georgian grape varieties and discuss available molecular insights on the resulting wines. The comparison of traditional European and traditional Georgian “qvevri” winemaking methods revealed that this method provides high antioxidant activity of Georgian wines, as well as a unique phenolic composition of red and white Georgian wines.