The aim of the study was to present a review of literature data on the antioxidant potential of raw milk and dairy products (milk, fermented products, and cheese) and the possibility to modify its level at the milk production and processing stage. Based on the available reports, it can be concluded that the consumption of products that are a rich source of bioactive components improves the antioxidant status of the organism and reduces the risk of development of many civilization diseases. Milk and dairy products are undoubtedly rich sources of antioxidant compounds. Various methods, in particular, ABTS, FRAP, and DPPH assays, are used for the measurement of the overall antioxidant activity of milk and dairy products. Research indicates differences in the total antioxidant capacity of milk between animal species, which result from the differences in the chemical compositions of their milk. The content of antioxidant components in milk and the antioxidant potential can be modified through animal nutrition (e.g., supplementation of animal diets with various natural additives (herbal mixtures, waste from fruit and vegetable processing)). The antioxidant potential of dairy products is associated with the quality of the raw material as well as the bacterial cultures and natural plant additives used. Antioxidant peptides released during milk fermentation increase the antioxidant capacity of dairy products, and the use of probiotic strains contributes its enhancement. Investigations have shown that the antioxidant activity of dairy products can be enhanced by the addition of plant raw materials or their extracts in the production process. Natural plant additives should therefore be widely used in animal nutrition or as functional additives to dairy products.