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Mathematical models for the spread of foot and mouth disease (FMD) have been developed and used for a number of purposes in the recent literature. One important purpose is predicting the effect of strategies to combat between-farm epidemic spread, in support of decision-making on epidemic control. The authors briefly review the various modelling approaches, discussing the parameters used and how estimates may be obtained for these parameters. They emphasise that, in addition to the estimation of FMD transmission parameters, the choice of model structure (including the number and type of parameters used) is also crucial. Two gaps in the knowledge of FMD transmission, related to model construction and parameter quantification, are identified: transmission between different species and the way in which vaccination affects such transmission, and route-specific FMD transmission properties. In particular, the authors pay attention to the role that small-scale transmission experiments can play in bridging these gaps.