Pomegranate (Punica granatum L.) is a fruit rich in bioactive compounds with various biological properties that help maintain good health. In particular, the polyphenolic compounds punicalagin, ellagic acid, urolithins and gallic acid are among the main molecules with antioxidant potential identified in this fruit; that is, these compounds have the ability to prevent cellular alterations caused by oxidative stress and/or induce the body’s own antioxidant response to protect cells. As a result, numerous scientific studies have emerged in the last decade, focused on recognizing the pharmacological properties of these molecules, to prevent the development and progression of diseases in which oxidative stress plays a fundamental role. The objectives of this review are: 1) to point out the importance of antioxidants obtained from the diet and in particular those obtained from pomegranate, 2) to highlight the beneficial effects of ellagitannins, ellagic acid, urolithins and gallic acid against various pathologies, and 3) recognize that despite their potential as therapeutic agents, further research in humans is required to promote their use in the clinic.