Several crop models may be used to simulate the effects of elevated CO2 on crop productivity. Yet no summary exists in the literature attempting to describe differences among models and how simulations might differ under climate change conditions. We provide an introductory review focusing on simulating the impacts of elevated CO2 on crops. We describe and discuss modeling approaches, component modules, applications to climate change and model validation and inter-comparison studies. By searching the recent peer-reviewed literature from 1995 to present, we found that about 20 f published crop modeling studies have focused on climate change impacts. About half of these studies explicitly analyzed the effects of elevated CO2 on crop growth and yield. Our analysis further suggested that the crop models that have been used the most in climate change assessments are also those that have been evaluated the least using available data from elevated CO2 experiments. Based on our review, we identify a set of recommendations aimed at improving our confidence in predictions of crop production under elevated CO2 and climate change conditions. These include continued model evaluation with existing field experiment data; increased focus on limiting factors such as pest, weeds, and disease; and attention to temporal and spatial scaling issues.