Our strategies for the treatment of cancer are constrained by our incomplete understanding of tumour biology and behaviour, and by the enormous complexity and resilience to therapeutic perturbation found in the biological world. We are obliged to simplify this complexity through the use of models and mechanistic explanations. In the first of these papers, we consider the nature of modelling mechanisms available to clinical researchers and the extent to which we rely upon them in our understanding of the nature and behaviour of tumours. In the second part, we will consider specifically how models help us to develop more effective strategies for cancer therapy. (C) 2000 Harcourt Publishers Ltd.</p