We report about a numerical approach based on the direct numerical simulation of the Navier–Stokes equations for the study of wave-bottom interaction problems. A Volume of Fluid (VOF) method is coupled with an Immersed Boundary Method (IBM) and applied to the simulation of propagating waves over complex shaped bottoms. We first investigate the flow induced by a solitary wave over generic bottoms (i.e. a semi-circular cylinder and a sloping beach). We show that the method is able to describe various important features of wave-bottom interactions, including flow separation, vortex shedding and wave breaking, while keeping a reasonable computational effort. Then we demonstrate the capability of the present approach to model arbitrary shaped bottoms by simulating the run-up of a breaking solitary wave over a natural beach profile.