  Exceptional points are singularities of eigenvalues and eigenvectors for
complex values of, say, an interaction parameter. They occur universally and
are square root branch point singularities of the eigenvalues in the vicinity
of level repulsions. The intricate connection between the distribution of
exceptional points and particular fluctuation properties of level spacing is
discussed. The distribution of the exceptional points of the problem
$H_0+\lambda H_1$ is given for the situation of hard chaos. Theoretical
predictions of local properties of exceptional points have recently been
confirmed experimentally. This relates to the specific topological structure of
an exceptional point as well as to the chiral properties of the wave functions
associated with exceptional points.
