The dielectric relaxation phenomena (dielectric losses) which are found in crystals and glasses in the region of 50 K (if measured with medium frequencies (103-106 s-1) must be assigned to local motions of ions. They show activation energies of the order of 0.1 eV. Two types of dielectric losses due to local motions can be distinguished: (1) The inherent dielectric losses due to local motions, since they are inherent to situations existing in the original crystal lattice or glass network; and (2) the induced dielectric losses due to local motions, since they are due to situations induced in the crystal lattice or the glass network, for instance by stress or radiation. There are also induced dielectric losses due to local motions of electrons, for instance in radiation induced colour centers. These losses show activation energies of the order of 0.01 eV. In this paper a number of cases described in the early as well as the recent literature is summed up and their physical background is discussed.