This paper introduces and discusses numerical methods for free-surface flow simulations and applies a large eddy simula- tion (LES) based free-surface-resolved CFD method to a couple of flows of hydraulic engineering interest. The advantages, dis- advantages and limitations of the various methods are discussed. The review prioritises interface capturing methods over interface tracking methods, as these have shown themselves to be more generally applicable to viscous flows of practical engineering interest, particularly when complex and rapidly changing surface topologies are encountered. Then, a LES solver that employs the level set method to capture free-surface deformation in 3-D flows is presented, as are results from two example calculations that conc com- plex low submergence turbulent flows over idealised roughness elements and bluff bodies. The results show that the method is capable of predicting very complex flows that are characterised by strong interactions between the bulk flow and the free-surface, and permits the identification of turbulent events and structures that would be very difficult to measure experimentally.