This Perspective describes advances from the author's laboratory on the free radical reactions of organic compounds with molecular oxygen. Polyunsaturated fatty acids (PUFAs) and sterols are particularly prone to undergo radical chain oxidation, and evidence suggests that this process, known as lipid peroxidation, occurs in vivo under a variety of conditions that are the result of an oxidative stress. Cyclic peroxides, hydroperoxides, and epoxy alcohols are major products formed from peroxidation, and the basic mechanisms of product formation are now reasonably well understood. These mechanisms include reversible addition of oxygen to carbon radicals, rearrangement and cyclization of allyl and pentadienyl peroxyl radicals, and homolytic substitution of carbon radicals on the peroxide bond. A physical organic approach to the problem of free radicals in biology and medicine is highlighted in this Perspective with stereochemical, kinetic, and extrathermodynamic probes applied to the study of mechanism. A radical clock permits the determination of free radical propagation rate constants, and 7-dehydrocholesterol, the immediate biosynthetic precursor of cholesterol, is found by this clock to be one of the most oxidizable lipids known. The consequences of the extreme reactivity of 7-dehydrocholesterol on human health is the focus of a current research theme in the author's laboratory.