Climate change could pose a major challenge to efforts towards strongly increase food production over the coming decades. However, model simulations of future climate-impacts on crop yields differ substantially in the magnitude and even direction of the projected change. Combining observations of current maximum-attainable yield with climate analogues, we provide a complementary method of assessing the effect of climate change on crop yields. Strong reductions in attainable yields of major cereal crops are found across a large fraction of current cropland by 2050. These areas are vulnerable to climate change and have greatly reduced opportunity for agricultural intensification. However, the total land area, including regions not currently used for crops, climatically suitable for high attainable yields of maize, wheat and rice is similar by 2050 to the present-day. Large shifts in land-use patterns and crop choice will likely be necessary to sustain production growth rates and keep pace with demand.