Basically, sand dunes are patterns resulting from the coupling of hydrodynamic and sediment transport. Once grains move, they modify the surface topography which in turns modifies the flow. This important feedback mechanism lies at the core of continuous dune modelling. Here we present an updated review of such a model for aeolian dunes, including important modifications to improve its predicting power. For instance, we add a more realistic wind model and provide a self-consistent set of parameters independently validated. As an example, we are able to simulate realistic barchan dunes, which are the basic solution of the model in the condition of unidirectional flow and scarce sediments. From the simulation, we extract new relations describing the morphology and dynamics of barchans that compare very well with existing field data. Next, we revisit the problem of the stability of barchan dunes and argue that they are intrinsically unstable bed-forms. Finally, we perform more complex simulations: first, a barchan dune under variable wind strength and, second, barchan dune fields under different boundary conditions. The latter has important implications for the problem of the genesis of barchan dunes. Copyright © 2010 John Wiley & Sons, Ltd.