  Recent studies demonstrated the violation of reciprocity in optical processes
in low-symmetry magnetic crystals. In these crystals the speed of light can be
different for counter-propagating beams. Correspondingly, they can show strong
directional anisotropies such as direction dependent absorption also called
directional dichroism[S. Bord\'acs et al., Nat. Phys. 8, 734 (2012); M. Saito
et al., J. Phys. Soc. Jpn. 77, 013705 (2008)]. Based on symmetry
considerations, we identify the magnetic point groups of materials which can
host such directional anisotropies and also provide a list of possible
candidate materials to observe these phenomena. In most of these cases, the
symmetry of the crystal allows directional anisotropy not only for optical
processes but also for the propagation of beams of particles and scalar waves.
We also predict new types of directional optical anisotropies -- besides the
optical magnetoelectric effect and the magnetochiral dichroism investigated so
far -- and specify the magnetic point groups of crystals where they can emerge.
