Around the world, wild boar or feral pigs are infected by a range of infectious organisms with important, productivity, public health or economic consequences. Consequently, the potential role of wild pigs in outbreaks of important exotic diseases, like foot-and-mouth disease (FMD), has been a significant consideration in many countries. Disease modelling is one means to study the epidemiology of disease and has been used to assess the potential role of wild pigs in FMD incursions. Many of these models have been strategic in nature. They have contributed to a broad understanding of disease control in wild pigs (e.g. the concept of threshold densities and the need to cull pigs below this density for disease fadeout to occur), but have not incorporated many of the key drivers affecting disease behaviour. Some of these drivers include important ecological, behavioural and geospatial relationships, such as interaction between different host species and the distribution, density and connectivity of pig populations. New approaches to modelling disease spread such as spatial simulation models use spatial data and explicitly incorporate geospatial relationships. These approaches can provide useful quantitative models that can be used to explore mitigation strategies under specific disease outbreak conditions. However, to date, most studies have been limited by inadequate data, and computational issues or have not explored mitigation strategies. To inform management strategies for emergency epidemics such as FMD in wild pigs, there is scope to further develop and use models to explore a range of incursion scenarios and investigate the efficacy of different mitigation strategies.