Organic peroxy radicals (often abbreviated RO(2)) play a central role in the chemistry of the Earth's lower atmosphere. Formed in the atmospheric oxidation of essentially every organic species emitted, their chemistry is part of the radical cycles that control the oxidative capacity of the atmosphere and lead to the formation of ozone, organic nitrates, organic acids, particulate matter and other so-called secondary pollutants. In this review, laboratory studies of this peroxy radical chemistry are detailed, as they pertain to the chemistry of the atmosphere. First, a brief discussion of methods used to detect the peroxy radicals in the laboratory is presented. Then, the basic reaction pathways - involving RO(2) unimolecular reactions and bimolecular reactions with atmospheric constituents such as NO, NO(2), NO(3), O(3), halogen oxides, HO(2), and other RO(2) species - are discussed. For each of these reaction pathways, basic reaction rates are presented, along with trends in reactivity with radical structure. Focus is placed on recent advances in detection methods and on recent advances in our understanding of radical cycling processes, particularly pertaining to the complex chemistry associated with the atmospheric oxidation of biogenic hydrocarbons.