Climate change is known to impact crop yields, mainly through increased temperatures, changing rainfall patterns and increasing CO2 concentration in the atmosphere. Although the potential effects of each of these factors have been discussed in a number of separate studies, no recent synthesis has been published to provide quantitative estimates of climate change impacts on crop yields, with or without adaptation strategies. In this paper, we synthetize a broad range of experimental or modeling studies to estimate, at the global scale, crop yield changes resulting from the marginal and combined effects of temperature, CO2 concentration and precipitation, with and without adaptation strategies. Crop yield sensitivities are estimated by distinguishing between C3 and C4 crops. For C3 crops, our results show that the positive effects of adaptation (+7.25 %) and CO2 (+9% for +100 ppm) are high enough to offset the negative effects of temperature increase (-2.4 % for +1 °C), even at +4 °C. On the other hand, for maize (i.e., the only C4 plant species in our database) the somewhat low positive effect from increased CO2 concentration and the absence of a significant effect of adaptation lead to higher yield losses, in the order of -10 % for +4 °C. The minimum level of CO2 concentration increase requested to achieve a yield gain under increased temperature conditions is much higher for maize than for C3 crops, in particular for wheat. The estimated effects of adaptation are uncertain, especially for soybean and rice, but also for maize, where the absence of a significant adaptation effect is probably at least partly due to limited data availability. Our results demonstrate that CO2 effects on crop yields should not be overlooked in foresight studies on the impacts of climate change. Our analysis also highlights the importance of improving our knowledge of how effective adapation strategies are in mitigating the impact of climate change.