The rhizosphere is a dynamic region where multiple interacting processes in the roots and surrounding soil take place, with dimensions set by the distance to which the zone of root influence spreads into the soil. Its complexity is such that some form of mathematical modelling is essential for understanding which of the various processes operating are important, and a minimal model of the rhizosphere must provide information on (a) the spatiotemporal concentration changes of mobile solutes in the root-influenced soil, and (b) the cumulative uptake of solutes per unit length of root over time. Both are unique for a given set of parameters and initial conditions and hence the model is fully deterministic. 'Up-scaling' to uptake by whole plants by integrating individual fluxes requires a measure of the growth and senescence of the root system. Root architecture models are increasingly successful in providing this. The spatio-temporal scales of the rhizosphere and roots are sufficiently different that they can be treated separately, and this greatly simplifies modelling. The minimal model has been successfully applied to the more-mobile nutrients in soil, such as nitrate or potassium, but much less successfully to less-soluble nutrients such as phosphorus, because other, undescribed processes become important. These include transfers from unavailable forms, heterogeneity of resource distribution, root competition, water redistribution and adaptive processes. Incorporating such processes into models can disrupt independent scaling. In general, scaling from the scale of the individual root to that of the whole plant does not pose insuperable problems. Paradoxically, the major challenge in introducing more complexity is that experimental corroboration of the model is required at the individual root scale.