The nematic phase of a liquid crystal is characterized by a global alignment of the molecules in a direction called the nematic director and an otherwise translational disorder. The strong opacity of the nematic phase comes about from local fluctuations of the nematic director that elastically scatter light. The strong scattering combined with the partial ordering of the nematic phase leads to an anisotropic diffusion process. There are several ways of combining nematics with either ordered (photonic crystals) or disordered (porous solids) dielectric structures. We have studied experimentally various aspects of anisotropic light diffusion, amongst which the anisotropy in the diffusion constant by means of time-resolved transmission experiments.