Abstract: There is great interest in the quantum/wave properties of systems that show chaos in the classical (short wavelength, or ray) limit. These wave chaotic systems appear in many contexts: nuclear physics, acoustics, two-dimensional quantum dots, and electromagnetic enclosures. Initiated by the need to understand the energy levels of complicated nuclei, random matrix theory (RMT) has been applied to successfully predict universal properties of these complicated wave-scattering systems through the statistical description of their eigenvalues, eigenfunctions, impedance matrices, and scattering matrices. For understanding the properties of practical systems, researchers at Maryland have developed the random coupling model (RCM) to offer a complete statistical model which utilizes a simple additive formula in terms of impedance matrices to combine the predictions of RMT and the nonuniversal system-specific features in practical systems. We have carried out experimental tests of the random coupling model in microwave cavities, including a superconducting microwave cavity acting as a low loss environment. The results demonstrate the nonuniversal features, such as the radiation impedance and the short orbits, and the universal fluctuations in wave properties, such as the scattering matrix elements and the impedance matrix elements, of complex wave scattering systems.