Most approaches to the modelling of crime - for predictive purposes or otherwise - are situated in continuous space; most commonly continuous 2D space or a simple grid system. The true structure of urban space, however, is substantially more complex than this, with both the natural and built environment playing a key role in its configuration. A fundamental determinant of this structure is the street network, which governs both the locations of places and the paths between them. Empirical research has established not only that crime risk varies according to the structural (i.e. graph-theoretic) characteristics of streets, but that dynamic crime phenomena such as clustering can also be observed at the street network level. This evidence, as well as a number of conceptual concerns, suggests that the street network may constitute a more meaningful, or effective, substrate for models of crime. Initial research in this area using statistical models indeed suggests that the use of the street network can improve the predictive performance of crime models, producing outputs which can be readily acted upon by police forces. Nevertheless, there have been few attempts to use such representations of space in the context of more formal mathematical models. This talk will outline the state of evidence in this area, demonstrate some network-based approaches, and suggest opportunities for ongoing research.