Global agriculture will, in the future, be faced with two main challenges: climate change and an increase in global food demand driven by an increase in population and changes in consumption habits. To be able to predict both the impacts of changes in climate on crop yields and the changes in agricultural practices necessary to respond to such impacts we currently need to improve our understanding of crop responses to climate and the predictive capability of our models. Ideally, what we would have at our disposal is a modelling tool which, given certain climatic conditions and agricultural practices, can predict the growth pattern and final yield of any of the major crops across the globe. We present a simple, process-based crop growth model based on the assumption that plants allocate above- and below-ground biomass to maintain overall carbon optimality and that, to maintain this optimality, the reproductive stage begins at peak nitrogen uptake. The model includes responses to available light, water, temperature and carbon dioxide concentration as well as nitrogen fertilisation and irrigation. The model is data constrained at two sites, the Yaqui Valley, Mexico for wheat and the Southern Great Plains flux site for maize and soybean, using a robust combination of space-based vegetation data (including data from the MODIS and Landsat TM and ETM instruments), as well as ground-based biomass and yield measurements. We show a number of climate response scenarios, including increases in temperature and carbon dioxide concentrations as well as responses to irrigation and fertiliser application.