  We review the main ideas and results in the stationary problems of quantum
chaos in generic (mixed) systems, whose classical dynamics has regular
(invariant tori) and chaotic regions coexisting in the phase space. First we
discuss the universality classes of spectral fluctuations (GOE/GUE for ergodic
systems, and Poissonian for integrable systems). We explain the problems in the
calculation of the invariant (Liouville) measure of classically chaotic
components, which has recently been studied by Robnik et al (1997) and by
Prosen and Robnik (1998). Then we describe the Berry-Robnik (1984) picture,
which is claimed to become exact in the strict semiclassical limit $\hbar\to
0$. However, at not sufficiently small values of $\hbar$ we see a crossover
regime due to the localization properties of stationary quantum states where
Brody-like behaviour with the fractional power law level repulsion is observed
in the corresponding quantal energy spectra.
