ABSTRACT: The time duration of a scattering process in quantum mechanics can be characterized by the so called Wigner delay time. Statistical approach to the scattering problems in mesoscopic physics is usually based on the random matrix theory (RMT). The application of the RMT is limited however to the situations where there are no non-trivial energy or length scales in the system. In this talk the opposite situation is considered. Namely, the statistical properties of the Wigner delay times are investigated for different models of disordered and chaotic systems exhibiting diffusion or localization.Wigner delay time: beyond the Random Matrix Theory