Increasing rates of global trade and travel, as well as changing climatic patterns, have led to more frequent outbreaks of plant disease epidemics worldwide. Mathematical modelling is a key tool in predicting where and how these new threats will spread, as well as in assessing how damaging they might be. Models can also be used to inform disease management, providing a rational methodology for comparing the performance of possible control strategies against one another. For emerging epidemics, in which new pathogens or pathogen strains are actively spreading into new regions, the spatial component of spread becomes particularly important, both to make predictions and to optimise disease control. In this chapter we illustrate how the spatial spread of emerging plant diseases can be modelled at the landscape scale via spatially explicit compartmental models. Our particular focus is on the crucial role of the dispersal kernel-which parameterises the probability of pathogen spread from an infected host to susceptible hosts at any given distance-in determining outcomes of epidemics. We add disease management to our model by testing performance of a simple "one off" form of reactive disease control, in which sites within a particular distance of locations detected to contain infection are removed in a single round of disease management. We use this simplified model to show how ostensibly arcane decisions made by the modeller-most notably whether or not the underpinning disease model allows for stochasticity (i.e. randomness)-can greatly impact on disease management recommendations. Our chapter is accompanied by example code in the programming language R available via an online repository, allowing the reader to run the models we present for him/herself.