Geometric optics is the study of high frequency solutions of hyperbolic partial differential equations. The solutions are described with rays and amplitudes. The amplitudes are the solutions of ordinary differential equations along rays. Such solutions resolve the classical wave-particle controversy in optics. In recent years some of the ideas have been extended to nonlinear hyperbolic partial differential equations. The resulting approximations reveal new qualitative behaviors as well as justifying a variety of ad hoc approximations in the scientific literature. The talk will describe some of the central ideas in the theory and some striking consequences.