We will discuss a canonical hyperbolic stratification of conformally flat
manifolds/orbifolds, especially with quasi-Fuchsian structures. Such
stratifications induce canonical totally geodesic laminations in the
initial hyperbolic manifold quasiconformallyequivalent to the
quasi-Fuchsian one. The main (open) problem is to understand how such
laminations can be used to deform corresponding hyperbolic structures into
quasi-Fuchsian ones. Also we will discuss our fresh results concerning the
situation of conformal structures and their discrete holonomy groups
generated by reflections.