The social, economic, and environmental costs of feeding a burgeoning and increasingly affluent human population will depend, in part, on how we increase crop production on under-yielding agricultural landscapes, and by how much. Such areas have a “yield gap” between the crop yields they achieve and the crop yields that could be achieved under more intensive management. Crop yield gaps have received increased attention in recent years due to concerns over land scarcity, stagnating crop yield trends in some important agricultural areas, and large projected increases in food demand. Recent analyses of global data sets and results from field trials have improved our understanding of where yield gaps exist and their potential contribution to increasing the food supply. Achieving yield gap closure is a complex task: while agronomic approaches to closing yield gaps are generally well-known, a variety of social, political, and economic factors allow them to persist. The degree to which closing yield gaps will lead to greater food security and environmental benefits remains unclear, and will be strongly influenced by the particular strategies adopted.