Intercropping is a farming practice involving two or more crop species, or genotypes, growing together and coexisting for a time. On the fringes of modern intensive agriculture, intercropping is important in many subsistence or low-input/resource-limited agricultural systems. By allowing genuine yield gains without increased inputs, or greater stability of yield with decreased inputs, intercropping could be one route to delivering 'sustainable intensification'. We discuss how recent knowledge from agronomy, plant physiology and ecology can be combined with the aim of improving intercropping systems. Recent advances in agronomy and plant physiology include better understanding of the mechanisms of interactions between crop genotypes and species - for example, enhanced resource availability through niche complementarity. Ecological advances include better understanding of the context-dependency of interactions, the mechanisms behind disease and pest avoidance, the links between above- and below-ground systems, and the role of microtopographic variation in coexistence. This improved understanding can guide approaches for improving intercropping systems, including breeding crops for intercropping. Although such advances can help to improve intercropping systems, we suggest that other topics also need addressing. These include better assessment of the wider benefits of intercropping in terms of multiple ecosystem services, collaboration with agricultural engineering, and more effective interdisciplinary research.