Astringency and bitterness are organoleptic properties widely linked to tannin compounds. Due to their significance to food chemistry, the food industry, and to human nutrition and health, these tannins’ taste properties have been a line of worldwide research. In recent years, significant advances have been made in understanding the molecular perception of astringency pointing to the contribution of different oral key players. Regarding bitterness, several polyphenols have been identified has new agonists of these receptors. This review summarizes the last data about the knowledge of these taste properties perceived by tannins. Ultimately, tannins’ astringency and bitterness are hand-in-hand taste properties, and future studies should be adapted to understand how the proper perception of one taste could affect the perception of the other one.