With the advent of synchrotron radiation, non-magnetic and magnetic resonant X-ray diffraction has become an important tool in modern materials research, e.g. on electronic states of systems. Polarized X-rays are sensitive to the local environments of resonant scattering atoms and their partial structures. At energies close to an absorption edge of an absorbing element, in particular, `forbidden' reflections can be excited, which would be extinct in absence of local anisotropic X-ray susceptibility. Anisotropy of energy-dependent susceptibility is treated in terms of tensor atomic scattering factors, giving rise to tensor structure factors, so that the intensity and polarization of the scattered radiation depend not only on the energy and polarization of the incident radiation, but also on both the crystal symmetry and the site symmetry. Owing to the anisotropy, rotation of the crystal about the scattering vector (azimuthal rotation) becomes an additional important parameter of investigation. This chapter considers the treatment and potential of anisotropic resonant scattering, both in the absence and presence of magnetic scattering, and the impact of symmetry on local physical properties, particularly symmetry and physical phenomena that allow and restrict forbidden reflections as well as reflections caused by magnetic scattering.