Abstract: This article first gives a brief review on thehistory of various approaches of modeling water waves basedon differing emphases on the main physical parameters involved.It presents a unified theory for modeling unsteady,three-dimensional, fully nonlinear and fully dispersivegravity-capillary waves in water of variable depth. Alsopresented is a Lagrangian-Eulerian hybrid numerical method forevaluating run-ups of nonlinear waves on sloping beach.Applications of these methods are illustrated with severalproblems of fundamental significance.