Antioxidants are omnipresent in nature and industry; they are used to slow down the autoxidative degradation of both organic tissues and petroleum‐derived products. Various mechanisms by which antioxidants can act are known, the most common of which are introduced here. Since autoxidation is a radical chain reaction, radical‐trapping antioxidants play a particularly important role; therefore, we will discuss these compounds in most detail. To introduce and develop central concepts relating to this topic, we present kinetic and thermodynamic data obtained for the reactions of phenols, the archetypical radical‐trapping antioxidants, with chain‐carrying peroxyl radicals, and describe the means to obtain these data. We then extend our discussion to other important classes of radical‐trapping antioxidants, beginning with the closely related polyphenols and newly developed pyridinol and pyrimidinol antioxidants, and then further to aromatic amines, organosulfur compounds, and their derivatives. We go on to touch upon the synergistic behavior in antioxidant combinations, and the effects of the medium on these interactions, and finally round things up with a few more important biological examples: ascorbate and β‐carotene. A few comments on the state of the field and areas requiring further research and development are included.