This paper considers how empirical models of urban housing markets might be constructed as a basis for policy analysis. It is suggested that this is fundamentally more difficult than national or regional models, because of particular characteristics of urban marketsnotably, the importance of social interactions, non-linearity and segregation. However, recent advances in the modelling of social interactions point to a possible way forward. The paper begins by reviewing some aspects of this literature and shows how the models generate non-linearities consistent with recent work on thresholds in local housing markets. Simple cellular automata are also used to demonstrate this point and how segregation may arise. A review follows of work on discrete choice models, which include social interactions within their structure. Bringing all the tools together, it is suggested that there is now the potential to construct urban housing models, although a great deal of theoretical and empirical work remains to be done.