The reaction of Criegee intermediates (CI) with NO and RO(2) radicals is studied for the first time by theoretical methodologies; additionally, the reaction of CI with SO(2) molecules is re-examined. The reaction of CI with NO was found to be slow, with a distinct energy barrier. Their reaction with RO(2) radicals proceeds by the formation of a pre-reactive complex followed by addition of the RO(2) radical on the CI carbon over a submerged barrier, leading to a larger peroxy radical and opening the possibility for oligomer formation in agreement with experiment. The impact of singlet biradicals on the reaction of CI with SO(2) is examined, finding a different reaction mechanism compared to earlier work. For larger CI, the reaction with SO(2) at atmospheric pressures mainly yields thermalized sulfur-bearing secondary ozonides. The fate of the CI in the atmosphere is examined in detail, based on observed concentration of a multitude of coreactants in the atmosphere, and estimated rate coefficients available from literature data. The impact of SCI on tropospheric chemistry is discussed.