The problem of modelling both the unsteady hydrodynamics and the topographical variations in natural channels is generally addressed by solving the de Saint Venant shallow water equations for the liquid phase together with the Exner sediment balance equation. This book focuses on the development of high order accurate centred schemes of the finite volume type for the numerical solution of the coupled de Saint Venant-Exner system. The schemes are tested by considering subcritical, supercritical, as well as transcritical flow conditions. They appear to correctly estimate the celerity of surface discontinuities as well of sediment bores and small bottom perturbations. The schemes are based on a simple centred approach, therefore they are certainly suitable for engineering purposes, often requiring simple numerical tools which can be easily used without addressing the mathematical details of the hyperbolic system of equations under consideration.