Future trajectories of food prices, food security, and cropland expansion are closely linked to future average crop yields in the major agricultural regions of the world. Because the maximum possible yields achieved in farmers' fields might level off or even decline in many regions over the next few decades, reducing the gap between average and potential yields is critical. In most major irrigated wheat, rice, and maize systems, yields appear to be at or near 80% of yield potential, with no evidence for yields having exceeded this threshold to date. A fundamental constraint in these systems appears to be uncertainty in growing season weather; thus tools to address this uncertainty would likely reduce gaps. Otherwise, short-term prospects for yield gains in irrigated agriculture appear grim without increased yield potential. Average yields in rainfed systems are commonly 50% or less of yield potential, suggesting ample room for improvement, though estimation of yield gaps for rainfed regions is subject to more errors than for irrigated regions. Several priorities for future research are identified.