Asymptotic and hybrid methods are widely used to compute the Radar Cross Section (RCS) of objects that are large compared to the wavelength of the incident wave, and the objective of this paper is to present an overview of a number of these methods. The cornerstone of the asymptotic methods is the Geometrical Theory of Diffraction (GTD), which was originally introduced by J. B. Keller, and which represents a generalization of the classical Geometrical Optics (GO) by virtue of the inclusion of diffraction phenomena. After a presentation of the physical principles of GTD, we provide a description of its mathematical foundations. In the process of doing this we point out that GTD gives inaccurate results at caustics and light-shadow boundaries, and subsequently present a number of alternate approaches to dealing with these problems, viz., Uniform theories; Methods for caustics curves; Physical Theory of Diffraction; and Spectral Theory of Diffraction. The effect of coating perfectly conducting bodies with dielectric materials is discussed and hybrid methods, that combine the Method of Moments (MoM) with asymptotic techniques, are briefly reviewed. Finally, the application of GTD and related techniques is illustrated by considering some representative radar targets of practical interest.>