Abstract. Random Matrices are powerful tools in many different areas of modern physics, ranging from nuclei, atoms and molecules over chaotic and disordered mesoscopic systems to quantum chromodynamics (theory of the strong interaction). By presenting a few examples, the usefulness of Random Matrices is explained. Moreover, it is shown why supersymmetric methods are nowadays so important in Random Matrix Theory. There is a natural extension of harmonic analysis on symmetric ordinary spaces to symmetric superspaces, connecting to the work of Harish-Chandra and Gelfand. Some group theoretical aspects are discussed. Finally, it is demonstrated that the supersymmetric approach also yields a natural extension of Calogero-Sutherland models for interacting particles.