Modelling evolution in a spatial continuum

We survey a class of models for spatially structured populations which we have called spatial A-Fleming-Viot processes. They arise from a flexible framework for modelling in which the key innovation is that random genetic drift is driven by a Poisson point process of spatial 'events'. We demonstrate how this overcomes some of the obstructions to modelling populations which evolve in two-(and higher-) dimensional spatial continua, how its predictions match phenomena observed in data and how it fits with classical models. Finally we outline some directions for future research.