Climate change challenges efforts to maintain and improve crop production in many regions. In this Review, we examine yield responses to warmer temperatures, elevated carbon dioxide and changes in water availability for globally important staple cereal crops (wheat, maize, millet, sorghum and rice). Elevated CO2 can have a compensatory effect on crop yield for C3 crops (wheat and rice), but it can be offset by heat and drought. In contrast, elevated CO2 only benefits C4 plants (maize, millet and sorghum) under drought stress. Under the most severe climate change scenario and without adaptation, simulated crop yield losses range from 7% to 23%. The adverse effects in higher latitudes could potentially be offset or reversed by CO2 fertilization and adaptation options, but lower latitudes, where C4 crops are the primary crops, benefit less from CO2 fertilization. Irrigation and nutrient management are likely to be the most effective adaptation options (up to 40% in wheat yield for higher latitudes compared with baseline) but require substantial investments and might not be universally applicable, for example where there are water resource constraints. Establishing multifactor experiments (including multipurpose cultivar panels), developing biotic stress modelling routines, merging process-based and data-driven models, and using integrated impact assessments, are all essential to better capture and assess yield responses to climate change.