Presented here for the first time are up-to-date reviews of a new and rapidly developing field of investigation: magnetic solids with polarized photons. The current experimental and theoretical fundamentals of the interplay of spin-orbit interaction and magnetism are described and recent advances in the understanding of the related spectroscopic phenomena are outlined. New aspects on a variety of methods are reported, covering magneto-optical Kerr-effect studies, spin- and angle-resolved photoemission spectroscopy, dichroism in X-ray near- and extended-edge absorption, and X-anomalous...