  We review recent developments on quantum scattering from mesoscopic systems.
Various spatial geometries whose closed analogs shows diffusive, localized or
critical behavior are considered. These are features that cannot be described
by the universal Random Matrix Theory results. Instead one has to go beyond
this approximation and incorporate them in a non-perturbative way. Here, we pay
particular emphasis to the traces of these non-universal characteristics, in
the distribution of the Wigner delay times and resonance widths. The former
quantity captures time dependent aspects of quantum scattering while the latter
is associated with the poles of the scattering matrix.
