We discuss Eulerian approaches to compute high frequency asymptotic solutions to wave phenomena including the solution to the Wave equations and the Schrodinger equations in the semi-classical regime. The talk will discuss methods including the geometrical optics, the Eulerian Gaussian beam method and a recently developed method which incorporating short-time WKBJ propagators into Huygen’s principle. These Eulerian are shown to be computationally very efficient and can yield accurate solutions even at caustics.