This paper will introduce the basic principles associated with hydraulic modelling of surface waters for geomorphological and hydrological purposes and illustrate how these have been applied to speci®c problems. The basic principles governing ¯uid ¯ow are derived from the principles of conservation of mass and momentum. In the case of the shallow ¯ow problems that typify most geomorphological and hydrological contexts, these equations involve some modi®cations: (i) as the boundary layer is likely to extend throughout the ¯ow depth, it is possible to assume a hydrostatic pressure distribution; (ii) special conditions need to be determined for both the bottom and water surface, including the possibility of horizontal gradients of atmospheric pressure for large-scale applications, and wind stress; and (iii) it is generally permissible to ignore the Coriolis terms. Direct application of the resultant equations is complicated by the need to Reynolds-average, which introduces additional terms but no additional equations. These terms have to be determined through empirical or semi-empirical transport equations, usually termed turbulence models. Current applications of these equations to geomorphological and hydrological applications are reviewed. Applications to river channels have generally not made use of the full three-dimensional form of the governing equations, and have either been one-dimensional, or, more commonly, two-dimensional. The latter involves depth averaging of the governing equations but requires parameterization of the eects of secondary circulation upon the transport of momentum. This has emphasized secondary circulation generated by curvature of the depth-averaged streamlines, but has yet to address secondary circulation associated with topographic discordance at river channel con¯uences or diuences or owing to anisotropic turbulence. Applications to unsteady ¯ows require special attention to be given to the eects of spatial and temporal variation in the depth of inundation, and the associated treatments are reviewed.