Intercropping is the cultivation of two or more crop species simultaneously in the same field, while relay intercropping means that the growing periods of the crop species are only partially overlapping. Intercropping has advantages with respect to productivity, resource capture, build-up of soil organic matter, and pest and disease suppression. This thesis aims to quantify and explain the yield advantages in wheat-maize relay intercropping and to assess the importance of intercropping for food production and land use efficiency. Wheat-maize intercropping had land equivalent ratios around or above one in two experiments in the Netherlands. Wheat in border rows showed major yield increases, and this yield increase was due to increases in the number of tillers per plant and the number of kernels per ear. The yield advantage of intercropped wheat was associated with a high radiation interception and radiation use efficiency (RUE). Under Dutch growing conditions, maize performance in the intercrop was constrained. Intercropping had a negative effect on the yield per plant and radiation use efficiency of maize. A strip intercrop model was developed, parameterized and tested with data on wheat-maize intercropping in the Netherlands. The model simulates radiation interception and growth in relay-strip intercrops with two species in different planting configurations. The model also allows simulating the consequences of border row effects for total system productivity. Bayesian analysis was applied to calibrate radiation use efficiency of wheat and maize in sole crops and intercrop. Intercropped wheat had higher a RUE than sole wheat, while intercropped maize had a lower RUE than sole maize. Intercropped maize had less favourable leaf traits (e.g. nitrogen content) during the flowering stage than sole maize in 2014, but the leaves in the intercrop had a higher photosynthetic rate than those in the sole crop. Possible explanations for this finding include differences between sole and mixed crops in water acquisition from soil, light distribution in the canopy, nitrogen distribution within the leaf and the contribution of the ear leaf to the growth of the cob. The low radiation use efficiency in intercropped maize may relate to nitrogen deficiency during grain filling. New concepts for potential yield, yield gain and yield gap in intercropping were developed in this thesis. Using crop model simulations and farm survey data, those concepts were operationalized in the context of wheat and maize production in an oasis area (Zhangye city) in northwest China. Wheat-maize intercropping resulted in substantial yield gains under potential and actual growing conditions. A comparison of potential and actual yields indicated a yield gap of 33% for sole wheat, 49% for sole maize, 15% for intercropped wheat, and 51% for intercropped maize. The land use analysis showed that discontinuing the use of intercropping in this region will decrease grain production substantially. Overall, this thesis studied the growth and productivity of wheat-maize intercropping at organ, plant and cropping system level, and also assessed its contribution to grain production at a regional level. The findings suggest that intercropping of food crops provides opportunities to meet increasing food demands. New technologies are needed to make strip intercropping efficient in terms of labour use and breeding should pay attention to cultivars that are suitable for intercropping.