This paper provides a review of stratosphere‐troposphere exchange (STE), with a focus on processes in the extratropics. It also addresses the relevance of STE for tropospheric chemistry, particularly its influence on the oxidative capacity of the troposphere. After summarizing the current state of knowledge, the objectives of the project Influence of Stratosphere‐Troposphere Exchange in a Changing Climate on Atmospheric Transport and Oxidation Capacity (STACCATO), recently funded by the European Union, are outlined. Several papers in this Journal of Geophysical Research–Atmospheres special section present the results of this project, of which this paper gives an overview. STACCATO developed a new concept of STE in the extratropics, explored the capacities of different types of methods and models to diagnose STE, and identified their various strengths and shortcomings. Extensive measurements were made in central Europe, including the first monitoring over an extended period of time of beryllium‐10 (¹⁰Be), to provide a suitable database for case studies of stratospheric intrusions and for model validation. Photochemical models were used to examine the impact of STE on tropospheric ozone and the oxidizing capacity of the troposphere. Studies of the present interannual variability of STE and projections into the future were made using reanalysis data and climate models.