  The phenomenon of super-radiance (Dicke effect, coherent spontaneous
radiation by a gas of atoms coupled through the common radiation field) is well
known in quantum optics. The review discusses similar physics that emerges in
open and marginally stable quantum many-body systems. In the presence of open
decay channels, the intrinsic states are coupled through the continuum. At
sufficiently strong continuum coupling, the spectrum of resonances undergoes
the restructuring with segregation of very broad super-radiant states and
trapping of remaining long-lived compound states. The appropriate formalism
describing this phenomenon is based on the Feshbach projection method and
effective non-Hermitian Hamiltonian. A broader generalization is related to the
idea of doorway states connecting quantum states of different structure. The
method is explained in detail and the examples of applications are given to
nuclear, atomic and particle physics. The interrelation of the collective
dynamics through continuum and possible intrinsic many-body chaos is studied,
including universal mesoscopic conductance fluctuations. The theory serves as a
natural framework for general description of a quantum signal transmission
through an open mesoscopic system.
