Radionuclides may be carried by groundwater from an underground waste repository to places accessible to man. The central role of mathematical modelling is to predict how their concentration varies in time at positions around the repository. This requires consideration of the physical and chemical processes at work and representation of the most important by mathematical expressions. As this can be done on several levels of detail both for water flow and radionuclide behaviour the resulting overall models can differ greatly in completeness and complexity. We discuss briefly some examples of such models, the data they require, the way these are gathered and how they have been used in practice. It is necessary to examine the validity of proposed models and we describe some approaches to this. We indicate the strengths and weaknesses of some commonly adopted models and outline current and future work aimed at improving our understanding.