Global grain production has increased dramatically during the past 50 years, mainly as a consequence of intensified land management and introduction of new technologies. For the future, a strong increase in grain demand is expected, which may be fulfilled by further agricultural intensification rather than expansion of agricultural area. Little is known, however, about the global potential for intensification and its constraints. In the presented study, we analyze to what extent the available spatially explicit global biophysical and land management-related data are able to explain the yield gap of global grain production. We combined an econometric approach with spatial analysis to explore the maximum attainable yield, yield gap, and efficiencies of wheat, maize, and rice production. Results show that the actual grain yield in some regions is already approximating its maximum possible yields while other regions show large yield gaps and therefore tentative larger potential for intensification. Differences in grain production efficiencies are significantly correlated with irrigation, accessibility, market influence, agricultural labor, and slope. Results of regional analysis show, however, that the individual contribution of these factors to explaining production efficiencies strongly varies between world-regions. © 2010 Elsevier Ltd. All rights reserved.