Biological systems are complex systems, almost by definition. Thus models of such systems necessarily simplify. That even simple models can lead to very complicated behaviour leads us to re-examine the goal of mathematical modelling. We may distinguish two loose categories of model: the “pure” model whose end is the understanding of phenomena, and the “applied” model directed to their control. Central to both is the notion of prediction, and it is this that is seen to be likely to be possible only to a limited degree. These matters are further compounded by the corresponding difficulty in solving the inverse problem of inferring the model from the phenomena. This leads us to query the way in which we might seek to understand the system (in the pure case) and to control it (in the applied one).