  This article is the written version of a talk delivered at the Bexbach
Colloquium of Science 2000 and starts with an introduction into quantum chaos
and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture
is formulated and evaluated within random-matrix theory. Several examples of
physical systems exhibiting quantum chaos ranging from nuclear to solid state
physics are presented. The presentation concludes with recent research work on
quantum chromodynamics and the quark-gluon plasma. In the case of a chemical
potential the eigenvalue spectrum becomes complex and one has to deal with
non-Hermitian random-matrix theory.
