The gas-phase oxidation of organic compounds is an important chemical process in the Earth's atmosphere. It governs oxidant levels and controls the production of key secondary pollutants, and hence has major implications for air quality and climate. Organic oxidation is largely controlled by the chemistry of a few reactive intermediates, namely, alkyl (R) radicals, alkoxy (RO) radicals, peroxy (RO2) radicals, and carbonyl oxides (R1R2COO), which may undergo a number of unimolecular and bimolecular reactions. Our understanding of these intermediates, and the reaction pathways available to them, is based largely on studies of unfunctionalized intermediates, formed in the first steps of hydrocarbon oxidation. However, it has become increasingly clear that intermediates with functional groups, which are generally formed later in the oxidation process, can exhibit fundamentally different reactivity than unfunctionalized ones. In this Perspective, we explore the unique chemistry available to functionalized organic intermediates in the Earth's atmosphere. After a brief review of the canonical chemistry available to unfunctionalized intermediates, we discuss how the addition of functional groups can introduce new reactions, either by changing the energetics or kinetics of a given reaction or by opening up new chemical pathways. We then provide examples of atmospheric reaction classes that are available only to functionalized intermediates. Some of these, such as unimolecular H-shift reactions of RO2 radicals, have been elucidated only relatively recently, and can have important impacts on atmospheric chemistry (e.g., on radical cycling or organic aerosol formation); it seems likely that other, as-yet undiscovered reactions of (multi)functional intermediates may also exist. We discuss the challenges associated with the study of the chemistry of such intermediates and review novel experimental and theoretical approaches that have recently provided (or hold promise for providing) new insights into their atmospheric chemistry. The continued use and development of such techniques and the close collaboration between experimentalists and theoreticians are necessary for a complete, detailed understanding of the chemistry of functionalized intermediates and their impact on major atmospheric chemical processes.