Atmospheric aerosol particles play pivotal roles in climate and air quality. Just as chemically reduced gases experience oxidation in the atmosphere, it is now apparent that solid and liquid atmospheric particulates are also subject to similar oxidative processes. The most reactive atmospheric gas-phase radicals, in particular the hydroxyl radical, readily promote such chemistry through surficial interactions. This Review looks at progress made in this field, discussing the radical-initiated heterogeneous oxidation of organic and inorganic constituents of atmospheric aerosols. We focus on the kinetics and reaction mechanisms of such processes as well as how they can affect the physico-chemical properties of particles, such as their composition, size, density and hygroscopicity. Potential impacts on the atmosphere include the release of chemically reactive gases such as halogens, aldehydes and organic acids, reactive loss of particle-borne molecular tracer and toxic species, and enhanced hygroscopic properties of aerosols that may improve their ability to form cloud droplets.