This study presents results of the Agricultural Model Intercomparison and Improvement Project (AgMIP) Coordinated Global and Regional Assessments (CGRA) of +1.5° and +2.0°C global warming above pre-industrial conditions. This first CGRA application provides multi-discipline, multi-scale, and multi-model perspectives to elucidate major challenges for the agricultural sector caused by direct biophysical impacts of climate changes as well as ramifications of associated mitigation strategies. Agriculture in both target climate stabilizations is characterized by differential impacts across regions and farming systems, with tropical maize experiencing the largest losses, while soy mostly benefits. The result is upward pressure on prices and area expansion for maize and wheat , while soy prices and area decline (results for rice are mixed). An example global mitigation strategy encouraging bioenergy expansion is more disruptive to land use and crop prices than the climate change impacts alone, even in the +2.0°C scenario which has a larger climate signal and lower mitigation requirement than the +1.5°C scenario. Coordinated assessments reveal that direct biophysical and economic impacts can be substantially larger for regional farming systems than global production changes. Regional farmers can buffer negative effects or take advantage of new opportunities via mitigation incentives and farm management technologies. Primary uncertainties in the CGRA framework include the extent of CO benefits for diverse agricultural systems in crop models, as simulations without CO benefits show widespread production losses that raise prices and expand agricultural area.