In the past, studies of stratosphere-troposphere exchange of mass and chemical species have mainly emphasized the synoptic- and small-scale mechanisms of exchange. This review, however, includes also the global-scale aspects of exchange, such as the transport across an isentropic surface (potential temperature about 380 K) that in the tropics lies just above the tropopause, near the 100-hPa pressure level. Such a surface divides the stratosphere into an “overworld” and an extratropical “lowermost stratosphere” that for transport purposes need to be sharply distinguished. This approach places stratosphere-troposphere exchange in the framework of the general circulation and helps to clarify the roles of the different mechanisms involved and the interplay between large and small scales. The role of waves and eddies in the extratropical overworld is emphasized. There, wave-induced forces drive a kind of global-scale extratropical “fluid-dynamical suction pump,” which withdraws air upward and poleward from the tropical lower stratosphere and pushes it poleward and downward into the extratropical troposphere. The resulting global-scale circulation drives the stratosphere away from radiative equilibrium conditions. Wave-induced forces may be considered to exert a nonlocal control, mainly downward in the extratropics but reaching laterally into the tropics, over the transport of mass across lower stratospheric isentropic surfaces. This mass transport is for many purposes a useful measure of global-scale stratosphere-troposphere exchange, especially on seasonal or longer timescales. Because the strongest wave-induced forces occur in the northern hemisphere winter season, the exchange rate is also a maximum at that season. The global exchange rate is not determined by details of near-tropopause phenomena such as penetrative cumulus convection or small-scale mixing associated with upper level fronts and cyclones. These smaller-scale processes must be considered, however, in order to understand the finer details of exchange. Moist convection appears to play an important role in the tropics in accounting for the extreme dehydration of air entering the stratosphere. Stratospheric air finds its way back into the troposphere through a vast variety of irreversible eddy exchange phenomena, including tropopause folding and the formation of so-called tropical upper tropospheric troughs and consequent irreversible exchange. General circulation models are able to simulate the mean global-scale mass exchange and its seasonal cycle but are not able to properly resolve the tropical dehydration process. Two-dimensional (height-latitude) models commonly used for assessment of human impact on the ozone layer include representation of stratosphere-troposphere exchange that is adequate to allow reasonable simulation of photochemical processes occurring in the overworld. However, for assessing changes in the lowermost stratosphere, the strong longitudinal asymmetries in stratosphere-troposphere exchange render current two-dimensional models inadequate. Either current transport parameterizations must be improved, or else, more likely, such changes can be adequately assessed only by three-dimensional models.