Autoxidation, the free radical chain reaction that nominally inserts O2 into hydrocarbons to give peroxides, is primarily responsible for the degradation of all organic materials. Peroxyl radicals propagate autoxidation mainly by abstraction of labile H-atoms from the hydrocarbons, whereas radical-trapping antioxidants (RTAs) inhibit autoxidation by donating an H-atom to the peroxyl radical to give a nonpropagating radical. As such, a detailed understanding of the kinetics and thermodynamics of H-atom transfer (HAT) reactions to peroxyl radicals, and the effects of sterics, electronics, and medium thereupon, is key to understanding the mechanisms and products of autoxidation and the ability of RTAs to inhibit it. Due to their relatively weak O-H and N-H bonds, phenols and aromatic amines have long been utilized as RTAs, but only phenols have been extensively optimized to maximize their reactivity. Amines offer greater structural variability owing to their trivalent central nitrogen atom. Simply linking the two aromatic rings of a diarylamine to afford a phenoxazine offers profound differences in HAT reactivity: 1000-times greater than diphenylamine and 10-fold more reactive than α-tocopherol, Nature's optimized phenolic RTA. Thus, phenoxazines are an exciting scaffold for RTA development. Indeed, we have recently shown that ring substitution of phenoxazine or 2,4-diazaphenoxazine can yield compounds that undergo barrierless HAT reactions with peroxyl radicals. Amines also have the distinct advantage that they can react with peroxyl radicals to yield nitroxides, which can inhibit autoxidation in a catalytic manner utilizing the substrate itself as the stoichiometric reductant. Herein we provide an account of our recent efforts to understand how they manage this feat, which have revealed at least four mechanisms depending on the specific reaction conditions (i.e., saturated hydrocarbons at elevated temperatures, unsaturated hydrocarbons, acidic media, aqueous media/lipid dispersions). We also reiterate how their impressive RTA activity translates from solution to mammalian cell culture, wherein we have demonstrated that diarylamines and their derived nitroxides are potent inhibitors of ferroptosis, a recently characterized form of cell death associated with lipid peroxidation (autoxidation). In addition to phenols and amines, organosulfur compounds have long been used as antioxidants. The prevailing view has been that they undergo ionic reactions with product peroxides, preventing the initiation of further chain reactions. In recent years, we have found that many organosulfur compounds exhibit very good RTA activity. In particular, sulfenic acids (RSOH) and hydropersulfides (RSSH) are found to be among the best HAT agents known, particularly to peroxyl radicals where secondary orbital interactions are found to play a significant role. Consequently, oxidation of the sulfenic acid to a sulfinic acid greatly diminishes its HAT reactivity to peroxyls. Polysulfides and their oxides also undergo direct reactions with peroxyl radicals, thereby inhibiting autoxidation, but do so by homolytic substitution reactions. These insights suggest that the RTA activity of organosulfur compounds may be as important to the inhibition of hydrocarbon autoxidation, if not more so, than their ionic reactions.