Stratosphere–troposphere exchange (STE) is important for the chemical composition of both the stratosphere and troposphere. Modifications of STE in a changing climate may affect stratospheric ozone depletion and the oxidizing capacity of the troposphere significantly. However, STE is still poorly understood and inadequately quantified, due to the involvement of physical and dynamical processes on local to global scales and to conceptual problems. In this study, a presentday global climatology of STE is developed that is based, from a data standpoint, on 15 yr of global meteorological reanalyses, and, from a conceptual standpoint, on a Lagrangian perspective that considers the pathways of exchange air parcels and their residence times in the troposphere and lowermost stratosphere. To this end, two complementary Lagrangian models are used. Particular consideration is given to “deep” exchange events that, through fast ascent of tropospheric or fast descent of stratospheric air masses, bring into contact air from the (potentially polluted) boundary layer and lower stratosphere. It is shown that they have different characteristics (strongly preferred geographical locations and a pronounced seasonal cycle) from that of the full set of exchange events. This result is important for accurately characterizing the effects of STE. In particular, it can be inferred that the well-documented springtime maximum of surface ozone cannot be explained primarily by STE.