Computational models are increasingly being used to assist in developing, implementing and evaluating public policy. This paper reports on the experience of the authors in designing and using computational models of public policy (‘policy models’, for short). The paper considers the role of computational models in policy making, and some of the challenges that need to be overcome if policy models are to make an effective contribution. It suggests that policy models can have an important place in the policy process because they could allow policy makers to experiment in a virtual world, and have many advantages compared with randomised control trials and policy pilots. The paper then summarises some general lessons that can be extracted from the authors’ experience with policy modelling. These general lessons include the observation that often the main benefit of designing and using a model is that it provides an understanding of the policy domain, rather than the numbers it generates; that care needs to be taken that models are designed at an appropriate level of abstraction; that although appropriate data for calibration and validation may sometimes be in short supply, modelling is often still valuable; that modelling collaboratively and involving a range of stakeholders from the outset increases the likelihood that the model will be used and will be fit for purpose; that attention needs to be paid to effective communication between modellers and stakeholders; and that modelling for public policy involves ethical issues that need careful consideration. The paper concludes that policy modelling will continue to grow in importance as a component of public policy making processes, but if its potential is to be fully realised, there will need to be a melding of the cultures of computational modelling and policy making.