Plant species mixtures improve productivity over monocultures by exploiting species complementarities for resource capture in time and space. Complementarity results in part from competition avoidance responses that maximize resource capture and growth of individual plants. Individual organs accommodate to local resource levels, e.g. with regard to nitrogen content and photosynthetic capacity or by size (e.g. shade avoidance). As a result, the resource acquisition in time and space is improved and performance of the community as a whole is increased. Modelling is needed to unravel the primary drivers and subsequent dynamics of complementary growth responses in mixtures. Here, we advocate using functional–structural plant (FSP) modelling to analyse the functioning of plant mixtures. In FSP modelling, crop performance is a result of the behaviour of the individual plants interacting through competitive and complementary resource acquisition. FSP models can integrate the interactions between structural and physiological plant responses to the local resource availability and strength of competition, which drive resource capture and growth of individuals in species mixtures. FSP models have the potential to accelerate mixed-species plant research, and thus support the development of knowledge that is needed to promote the use of mixtures towards sustainably increasing crop yields at acceptable input levels.