Numerical simulations have radically changed the way we predict and understand nonlinear gravity waves. In this talk, I will describe my personal experience in using computations to study a variety of nonlinear wave-wave and wave-body interaction problems focusing mainly on those where potential flow has shown to be remarkably successful. These range from earlier efforts to simulate steep plunging waves and their forces and impact on bodies to recent developments in the deterministic reconstruction and forecasting of very large scale nonlinear wave fields.