  Reviewing the semiclassical theory for the parametric level density
fluctuations, we show that for large parametric changes the density correlation
function, after rescaling, becomes universal and coincides with the leading
asymptotic term obtained from Random Matrix Theory. The advantage of the
semiclassical approach is to provide a simple recipe for the calculation of the
non-universal scaling parameter from elements of the underlying classical
dynamics specific to the system. We discuss recent improvements of the theory,
which introduce a requantization of the smoothed level density.
