  We discuss and briefly overview recent progress with studying fluctuations in
scattering on a resonance state coupled to the background of many chaotic
states. Such a problem arises naturally, e.g., when dealing with wave
propagation in the presence of a complex environment. Using a statistical model
based on random matrix theory, we obtain a number of nonperturbative results
for various statistics of scattering characteristics. This includes the joint
and marginal distributions of the reflection and transmission intensities and
phases, which are derived exactly at arbitrary coupling to the background with
finite absorption. The intensities and phases are found to exhibit highly
non-trivial statistical correlations, which remain essential even in the limit
of strong absorption. In the latter case, we also consider the relevant
approximations and their accuracy. As an application, we briefly discuss the
statistics of the phase rigidity (or mode complexness) in such a scattering
situation.
