A review is given of a wide variety of asymptotic methods used in high-frequency scattering. Following brief descriptions of the saddle point method, Watson transformation, and residue series, a survey of the literature is made in which these methods have been employed. The desirability of using high-frequency approximate methods is pointed out. A critical discussion of geometrical optics, physical optics, and the geometrical theory of diffraction is presented. The relationship of these methods to the asymptotic solution of Maxwell's equations is examined. Their applicability and limitations are discussed by referring to numerous examples in the literature.