Dioscorea, consisting of over 600 species, is the most important genus in the Dioscoreaceae family; however, the practically used plants, which are commonly called yam, are restricted to a remarkably smaller number of species. Numerous studies have reported the high nutritional value of yam, particularly as an alternative source of starch and some important micronutrients. Several Dioscorea species are widely used for various medicinal purposes as well. In many studies, the bioactivities and health benefits of Dioscorea extracts and other preparations have been related to the presence of phytochemicals, which possess antioxidant properties; they are related mainly to radical-scavenging capacity in chemical assays and positive effects on the endogenous antioxidant system in cell-based and in vivo assays. Considering the increasing number of publications on this topic and the absence of comprehensive and focused review papers on antioxidant potential, this article summarizes the results of studies on the antioxidant properties of Dioscorea spp. and their relation to phytochemicals and health benefits. A comprehensive survey of the published articles has revealed that the majority of studies have been performed with plant tubers (rhizomes, roots), while reports on leaves are rather scarce. In general, leaf extracts demonstrated stronger antioxidant potential than tuber preparations. This may be related to the differences in phytochemical composition: saponins, phenanthrenes and, for some pigment-rich species (purple yams), anthocyanins are important constituents in tubers, while phenolic acids and flavonoids are characteristic phytochemicals in the leaves. The review may assist in explaining ethnopharmacological knowledge on the health benefits of Dioscorea plants and their preparations; moreover, it may foster further studies of poorly investigated species, as well as their wider application in developing new functional foods and nutraceuticals.