The delivery of essential ecosystem functions (primary productivity, maintenance of soil fertility, resistance to weed invasion etc.) may be compromised by global declines in biodiversity. There is still controversy about the description of, and mechanisms behind, Biodiversity-Ecosystem Function (BEF) relationships. The Diversity-Interactions model quantified BEF relationships in terms of all the pairwise interactions between the species in a community. The model gives the contribution of two species (i and j) to the functional response in a community as _ijPiPj, where _ij reflects the potential of the two species to contribute to the response and its actual contribution depends also on Pi and Pj, the initial relative abundance of the two species in the community. This model and variants fitted well to a wide range of functional responses (biomass production, respiration) from several, but not all, experiments that examined a wide range of organisms (plants, microorganisms) and levels of species richness (1 to 72 species). A modified version introduces a more complex effect of pairwise interaction. The properties of this more flexible model and its implications for BEF relationships are discussed, particularly in the context of grass-clover contributions to sward functions.