Crop growth models dynamically simulate processes of C, N and water balance on daily or hourly time-steps to predict crop growth and development and at season-end, final yield. Their ability to integrate effects of genetics, environment and crop management have led to applications ranging from understanding gene function to predicting potential impacts of climate change. The history of crop models is reviewed briefly, and their level of mechanistic detail for assimilation and respiration, ranging from hourly leaf-to-canopy assimilation to daily radiation-use efficiency is discussed. Crop models have improved steadily over the past 30–40 years, but much work remains. Improvements are needed for the prediction of transpiration response to elevated CO2 and high temperature effects on phenology and reproductive fertility, and simulation of root growth and nutrient uptake under stressful edaphic conditions. Mechanistic improvements are needed to better connect crop growth to genetics and to soil fertility, soil waterlogging and pest damage. Because crop models integrate multiple processes and consider impacts of environment and management, they have excellent potential for linking research from genomics and allied disciplines to crop responses at the field scale, thus providing a valuable tool for deciphering genotype by environment by management effects.