The antioxidant activity of protein-derived peptides was one of the first to be revealed among the more than 50 known peptide bioactivities to date. The exploitation value associated with food-derived antioxidant peptides is mainly attributed to their natural properties and effectiveness as food preservatives and in disease prevention, management, and treatment. An increasing number of antioxidant active peptides have been identified from a variety of renewable sources, including terrestrial and aquatic organisms and their processing by-products. This has important implications for alleviating population pressure, avoiding environmental problems, and promoting a sustainable shift in consumption. To identify such opportunities, we conducted a systematic literature review of recent research advances in food-derived antioxidant peptides, with particular reference to their biological effects, mechanisms, digestive stability, and bioaccessibility. In this review, 515 potentially relevant papers were identified from a preliminary search of the academic databases PubMed, Google Scholar, and Scopus. After removing non-thematic articles, articles without full text, and other quality-related factors, 52 review articles and 122 full research papers remained for analysis and reference. The findings highlighted chemical and biological evidence for a wide range of edible species as a source of precursor proteins for antioxidant-active peptides. Food-derived antioxidant peptides reduce the production of reactive oxygen species, besides activating endogenous antioxidant defense systems in cellular and animal models. The intestinal absorption and metabolism of such peptides were elucidated by using cellular models. Protein hydrolysates (peptides) are promising ingredients with enhanced nutritional, functional, and organoleptic properties of foods, not only as a natural alternative to synthetic antioxidants.