Model-predictive control (MPC) has recently excited a great deal of interest as a new control paradigm for non-domestic buildings. Since it is based on the notion of optimisation, MPC is, in principle, well-placed to deliver significant energy savings and reduction in carbon emissions compared to existing rule-based control systems. In this paper, we critically review the prospects for buildings MPC and, in particular, the central role of the predictive mathematical model that lies at its heart; our clear emphasis is on practical implementation rather than control-theoretic aspects, and covers the role of occupants as well as the form of the predictive model. The most appropriate structure for such a model is still an open question, which we discuss alongside the development of the initial model, and the process of updating the model during the building's operational life. The importance of sensor placement is highlighted alongside the possibility of updating the model with occupants' comfort perception. We conclude that there is an urgent need for research on the automated creation and updating of predictive models if MPC is to become an economically-viable control methodology for non-domestic buildings. Finally, more evidence through operating full scale buildings with MPC is required to demonstrate the viability of this method.