Using a newly-available panel dataset of gridded annual crop yields in conjunction with a dynamic econometric model that distinguishes between farmers' short-run and long-run responses to weather shocks and accounts for adaptation, we investigate the risk to global crop yields from climate warming. Over broad spatial domains we observe only slight moderation of short-run impacts by farmers' long-run adjustments. In the absence of additional margins of adaptation beyond those pursued historically, projections constructed using an ensemble of 21 climate model simulations suggest that the climate change could reduce global crop yields by 3–12% by mid-century and 11–25% by century's end, under a vigorous warming scenario.