Predicted changes in atmospheric composition and climate affecting crop productivity are reviewed. These include changes in both average conditions and extreme events, with respect to temperature, drought, flooding and surface ozone, coupled with rising atmospheric [CO2]. Impacts on, and means to adapt, crops to these changes are reviewed and outlined. Particular emphasis is given to (i) the results from open air field manipulations of surface atmosphere, temperature and soil water to understand impacts and adaptation and (ii) demonstrated genetic manipulations of photosynthesis and water use that could support future food supply under current and future conditions. Finally, attention is given to means by which crop systems could serve as CO2 collectors and carbon storage systems. Here, apparent opportunities are outlined for (i) manipulations of crops to enhance carbon storage and (ii) use of high-productivity sustainable perennial C4 grasses coupled with carbon capture and storage. This article is part of the theme issue ‘Crops under stress: can we mitigate the impacts of climate change on agriculture and launch the ‘Resilience Revolution’?’.