  The application of random-matrix theory (RMT) to compound-nucleus (CN)
reactions is reviewed. An introduction into the basic concepts of nuclear
scattering theory is followed by a survey of phenomenological approaches to CN
scattering. The implementation of a random-matrix approach into scattering
theory leads to a statistical theory of CN reactions. Since RMT applies
generically to chaotic quantum systems, that theory is, at the same time, a
generic theory of quantum chaotic scattering. It uses a minimum of input
parameters (average S-matrix and mean level spacing of the CN). Predictions of
the theory are derived with the help of field-theoretical methods adapted from
condensed-matter physics and compared with those of phenomenological
approaches. Thorough tests of the theory are reviewed, as are applications in
nuclear physics, with special attention given to violation of symmetries
(isospin, parity) and time-reversal invariance.
