During the life of aerobic organisms, the oxygen resulting from numerous reactions is converted into reactive oxygen species (ROS). Many ROS are dangerous due to their high reactivity; they are strong oxidants, and react with various cell components, leading to their damage. To protect against ROS overproduction, enzymatic and non-enzymatic systems are evolved in aerobic cells. Several known non-enzymatic antioxidants have a relatively low specific antioxidant activity. Superoxide dismutases, catalase, glutathione peroxidase, glutathione S-transferase, thioredoxin, and the peroxiredoxin families are the most important enzyme antioxidants. Artificial antibodies catalyzing redox reactions using different approaches have been created. During the past several decades, it has been shown that the blood and various biological fluids of humans and animals contain natural antibodies that catalyze different redox reactions, such as classical enzymes. This review, for the first time, summarizes data on existing non-enzymatic antioxidants, canonical enzymes, and artificial or natural antibodies (abzymes) with redox functions. Comparing abzymes with superoxide dismutase, catalase, peroxide-dependent peroxidase, and H2O2-independent oxidoreductase activities with the same activities as classical enzymes was carried out. The features of abzymes with the redox activities are described, including their exceptional diversity in the optimal pH values, dependency and independence on various metal ions, and the reaction rate constants for healthy donors and patients with different autoimmune diseases. The entire body of evidence indicates that abzymes with redox antioxidant activities existing in the blood for a long time compared to enzymes are an essential part of the protection system of humans and animals from oxidative stress.