Cucurbitaceae is one of the most economically important plant families, and includes some worldwide cultivated species like cucumber, melons, and squashes, and some regionally cultivated and feral species that contribute to the human diet. For centuries, cucurbits have been appreciated because of their nutritional value and, in traditional medicine, because of their ability to alleviate certain ailments. Several studies have demonstrated the remarkable contents of valuable compounds in cucurbits, including antioxidants such as polyphenols, flavonoids, and carotenoids, but also tannins and terpenoids, which are abundant. This antioxidant power is beneficial for human health, but also in facing plant diseases and abiotic stresses. This review brings together data on the antioxidant properties of cucurbit species, addressing the genetic and pre- and postharvest factors that regulate the antioxidant content in different plant organs. Environmental conditions, management, storage, and pre- and postharvest treatments influencing the biosynthesis and activity of antioxidants, together with the biodiversity of this family, are determinant in improving the antioxidant potential of this group of species. Plant breeding, as well as the development of innovative biotechnological approaches, is also leading to new possibilities for exploiting cucurbits as functional products.