In this short course we will review the most popular approaches to the numerical integration of the fully nonlinear water wave equations. More specifically, the lectures willl cover the boundary integral equation method (BIEM), higher order spectral methods (HOS), the Dirichlet-to-Neumann operator approach, the conformal mapping technique and finally the smoothed particle hydrodynamics method (SPH). The advantages and shortcomings of the different methods will be discussed as well. Applications will be presented.