The combination of drugs is a common practice for enhancing the efficiency of drug treatment, but selection of the optimal combination and the optimal doses remains a matter of trial and error. Prediction of synergistic, additive and antagonistic responses to drug combinations in vivo is therefore of considerable interest. The present review discusses the application of mathematical and statistical models to assess combined drug action by response surface modelling. The most commonly applied models are designed to distinguish between synergistic and additive responses on the basis of a single parameter to indicate whether a drug combination acts synergistic or not. It is, however, recognized that these relatively simple models often do not adequately describe complex drug interactions. This has led to the application of increasingly complex models with multiple drug interaction parameters that can describe a wide range of synergistic and antagonistic responses in a single-response surface. The capability to describe response surfaces with high resolution offers the opportunity to develop an understanding of the mechanisms that underlie the observed combined drug response. Operational models for drug interaction constitute a highly versatile framework for mechanism-based modelling by taking the signal transduction properties of the drug combination into account. On this basis, it is predicted that the occurrence of synergism is favoured by convergence of drug signals late in the signal transduction pathway as opposed to proximal convergence. Furthermore, a high efficiency of signal transduction poses in general a barrier to the occurrence of synergism. The in vivo application of operational models with advanced response surface modelling techniques will facilitate the rational development of synergistic drug combinations.