Nowadays, human society appropriates about one quarter of total net primary production of the terrestrial biosphere. Production of food, energy and materials, and the related use of land and water account for crucial components and interactions in the Earth System. However, rising food, energy and material demand, climate change and ambitious mitigation policies will enhance the competition for land and water. While the combined impacts of these drivers are still highly uncertain, global land-use patterns will change in the future, reacting to these pressures. Projecting their future development is important to study both, their impacts on the Earth System as well as the limitations of land use since freshwater and fertile land are only available in limited amounts. The challenge of projecting future land-use patterns is to account, within one modeling framework, for the socio-economic determinants of agricultural demand as well as for the spatial heterogeneity of the land’s suitability for agricultural production. In order to simulate these combined effects in a spatially explicit way, we present a Model of Agricultural Production and its Impact on the Environment (MAgPIE). MAgPIE is a mathematical programming model covering the most important food and feed, livestock and bioenergy production types in 10 economic regions worldwide. It takes regional economic conditions as well as spatially explicit data on potential crop yields, land and water constraints from a global process-based vegetation model (LPJmL) that covers also the full hydrological cycle into account and derives specific land-use patterns for each grid cell. Implicit economic values (shadow prices) for binding constraints can be used to valuate resources for which in many places no markets exist, especially irrigation water and different types of technological change in agricultural production are included. In this presentation we describe the model structure and validation. We apply the model to possible future scenarios up to 2055 and derive required rates of technological change (i.e. yield increase) in agricultural production in order to meet future food demand.