Universal statistical aspects of wave scattering by a variety of physical systems ranging from atomic nuclei to mesoscopic systems and microwave cavities are described. A statistical model for the scattering matrix, introduced in the past in the context of nuclear physics, is employed to address the problem of quantum chaotic scattering. The main application of the model is the analysis of electronic transport through ballistic mesoscopic cavities: it describes well the results from the numerical solutions of the Schrödinger equation for two-dimensional systems. © 2002 Published by Elsevier Science B.V.