Classical models for gene flow fail in (at least) three ways. First, they cannot explain patterns in data observed over large scales; second, they predict much more genetic diversity than is observed; and third, they asssume that genetic loci evolve independently. I shall describe, as time permits, results of joint projects with Nick Barton, Nathanael Berestycki, Jerome Kelleher and Amandine Veber in which we have proposed a framework for modelling populations that are distributed across a spatial continuum and analysed aspects of a particular model that arises in this framework that we have called the spatial Lambda-Fleming-Viot process.