Plant responses to rising atmospheric carbon dioxide (CO2) concentrations, together with projected variations in temperature and precipitation will determine future agricultural production. Estimates of the impacts of climate change on agriculture provide essential information to design effective adaptation strategies, and develop sustainable food systems. Here, we review the current experimental evidence and crop models on the effects of elevated CO2 concentrations. Recent concerted efforts have narrowed the uncertainties in CO2-induced crop responses so that climate change impact simulations omitting CO2 can now be eliminated. To address remaining knowledge gaps and uncertainties in estimating the effects of elevated CO2 and climate change on crops, future research should expand experiments on more crop species under a wider range of growing conditions, improve the representation of responses to climate extremes in crop models, and simulate additional crop physiological processes related to nutritional quality.