Antioxidant peptides extracted from natural foods have been studied for their potential use in the development of additives, nutraceuticals, and therapeutic agents. Nut proteins are considered an excellent source of plant-derived proteins for the human diet, due to their high protein content and digestibility of up to 86.22%. Furthermore, compared with grain and soybean proteins, nut proteins have a special amino acid composition, which makes their protein structure different, and promotes their disparate functional characteristics and great bioactivity potential. This review presents the most remarkable studies on antioxidant peptides from nuts, to gain insights into feasible production methods, different evaluation indexes within in vivo or in vitro systems, high bioavailability, and the complex structure-activity relationship resulting from the particularity of their protein structure and amino acid composition. Previously published studies mainly focused on the effects of the production methods/processes of nut-derived peptides on antioxidant activity, and proved that nut-extracted antioxidant peptides can resist the degradation of acid, alkali, and gastrointestinal enzymes, have high antioxidant activity in vitro and in vivo, and also have the potential to cross small intestinal epithelial cells in a stable and integral manner. However, the structure-activity relationship of antioxidant peptides from nuts has not been fully established, and the structure information of antioxidant peptides obtained from various nut protein sources is still unclear. The findings presented in this review can be used to provide the theoretical basis for the design and production of nut-derived antioxidant peptides.