We review current observational and theoretical knowledge of the stratospheric aerosols. These particles, which are composed primarily of sulfuric acid and other sulfates, are concentrated in a layer extending 20 km or more above the tropopause. The aerosols affect the chemistry of the stratosphere and the climatology of the earth. A number of important chemical and physical roles for the aerosols are discussed. We describe the properties of stratospheric aerosols as revealed by experimental data. Remote-sensing optical instruments, both active (lidars) and passive (satellites), allow routine mapping of the global aerosol distribution. Extensive in situ measurements obtained by mechanical collection (filters and impactors) and scattered-light detection yield the overall size dispersion of the aerosols. Laboratory analyses of preserved aerosol samples define the bulk composition (and possible origins) of the particles. Quantitative studies of aerosol precursor gases (SO2, OCS, and CS2) by wet chemical, cryogenic, and spectroscopic techniques reveal the photochemical sources of particulate mass. Theoretical aspects of the stratospheric aerosols are also reviewed. We discuss aerosol chemical reactions including those of gaseous precursors, those i n aqueous solution, and thos e on particle surfaces. We also describe aerosol microphysical processes including nucleation, condensation/ evaporation, coagulation, and sedimentation. Existing models of aerosols which incorporate these chemical and physical processes are outlined. Aerosol model predictions are appraised vis h vis observations. The simulations are shown to agree with measurements in many important respects. Areas requiring further investigation include the identification of the nucleation mechanisms for the aerosols and the characterization of the tenuous upper extent of the aerosol layer above ---25 km. Estimates are presented for the potential aerosol changes attributable to the emissions of particles and gases by aerospace operations (aircraft and rockets) and industrial consumption of fossil fuels. It is demonstrated that although the climatic effects of existing levels of stratospheric aerosol pollution are negligible, potential increases in those levels might pose a future threat. Evidence for a major influence of massive volcanic eruptions on terrestrial climate is discussed. Model calculations of climate perturbations associated with past volcanic activity are summarized. In addition, detailed physico-