  We study quantum transport in anisotropic 3D disorder and show that non
rotation invariant correlations can induce rich diffusion and localization
properties. For instance, structured finite-range correlations can lead to the
inversion of the transport anisotropy. Moreover, working beyond the
self-consistent theory of localization, we include the disorder-induced shift
of the energy states and show that it strongly affects the mobility edge.
Implications to recent experiments are discussed.
