Responses of global crop yields to warmer temperatures are fundamental to sustainable development under climate change but remain uncertain. Here, we combined a global dataset of field warming experiments (48 sites) for wheat, maize, rice and soybean with gridded global crop models to produce field-data-constrained estimates on responses of crop yield to changes in temperature (S-T) with the emergent-constraint approach. Our constrained estimates show with >95% probability that warmer temperatures would reduce yields for maize (-7.1 +/- 2.8% K-1), rice (-5.6 +/- 2.0% K-1) and soybean (-10.6 +/- 5.8% K-1). For wheat,S(T)was 89% likely to be negative (-2.9 +/- 2.3% K-1). Uncertainties associated with modelledS(T)were reduced by 12-54% for the...