Compact Ranges are widely used for antenna measurements across wide frequency ranges spanning frequencies as low as 350MHz to as high as 60GHz and above. Advances in electromagnetic (EM) simulations have significantly improved the design process for compact ranges, resulting in reduced costs. Asymptotic methods such as Geometrical Optics (GO), Physical Optics (PO) are widely used due their reduced simulation costs for electrically large reflectors used in compact range design. With advances in availability of computer hardware, full wave methods such as Method of Moments (MoM), Adaptive Cross Approximation (ACA), and Multilevel Fast Multipole Method (MLFMM) can be used for more accurate analysis of compact ranges within reasonable simulation cost. In this paper, we will review computational techniques that are becoming popular to analyze compact ranges. Accuracy of simulations using full wave and asymptotic techniques will be presented.