Achieving and maintaining global food security is challenged by changes in population, income, and climate, among other drivers. Assessing these threats and weighing possible solutions requires a robust multidisciplinary approach. One such approach integrates biophysical modeling with economic modeling to explore the combined effects of climate stresses and future socioeconomic trends, thus providing a more accurate picture of how agriculture and the food system may be affected in the coming decades. We review and analyze the literature on this structural approach and present a case study that follows this methodology, explicitly modeling drought and heat tolerant crop varieties. We show that yield gains from adoption of these varieties differ by technology and region, but are generally comparable in scale to (and thus able to offset) adverse effects of climate change. However, yield increases over the projection period are dominated by the effects of growth in population, income, and general productivity, highlighting the importance of joint assessment of biophysical and socioeconomic drivers to better understand climate impacts and responses.