Studies of radiation damage in crystalline insulators usually originate from problems connected with heavy ion impact during ion bombardment, from neutron irradiation with and without fission in nuclear reactors, or from α-decay with the resulting damage due to recoil daughter atoms of the decaying nuclei of actinide compounds. The materials involved cover a broad range of compounds, e.g. from BeO to CmO2for oxides, for which most work has been done. The damage studied ranges from production of isolated Frenkel pairs to complete amorphization of the crystalline compound (metamictization). The available knowledge is discussed. Emphasis is put on simple binary oxides and on ceramic nuclear fuel materials, i.e. oxides, carbides and nitrides of U and Pu. Recent work on irradiated glasses is also briefly discussed since these glasses are considered as promising media for safe storage of radioactive waste for long periods of time.