Radiation‐induced defects and their annealing behavior inp‐ andn‐type CdTe irradiated with 2‐MeV electrons, neutrons, and60Co gamma rays have been investigated by means of photoluminescence, Hall, time‐of‐flight measurements, and the performance of CdTe gamma‐ray detectors. The 1.1‐eV emission band produced after electron irradiation at 77 K anneals at a stage centered around about 120 K and originates from a defect including Te vacancy. From the isothermal annealing experiment, an activation energy of about 0.2 eV is obtained for the annealing stage. The electron and gamma irradiation at 77 K with room‐temperature anneal, and neutron irradiation at 300 K enhance 1.53‐ and 1.55‐eV edge emission bands. It has been suggested that the 1.53‐eV band is attributed to a complex involving Cd vacancies. On the other hand, the 1.55‐eV band is attributed to a complex involving Te vacancies. An annealing stage centered at about 370 K is observed in electrical properties in relatively purep‐type crystals irradiated with electrons and gamma rays. It is found from the isothermal annealing that the annealing behavior of the stage obeys first‐order kinetics. The activation energy for the migration of the defects is estimated to be about 0.8 eV and the pre‐exponential factor is found to be about 108sec−1, suggesting long‐range migration of Cd vacancies. Electron‐trap levels lying at 0.058 and 0.5 eV below the conduction band are observed in crystals irradiated with gamma rays. The 0.058‐eV electron trap anneals at about 600 K and the origin is tentatively assigned to a complex involving Te vacancies as inferred from photoluminescence results. Electron‐drift mobility at room temperature is remarkably reduced after gamma irradiation, possibly due to the introduction of an electron‐trap level at about 0.5 eV below the conduction band. The 0.5‐eV electron‐trap level and the electron‐drift mobility anneal in the vicinity of about 600 K. The effects due to successive detector irradiations with60Co gamma rays markedly degraded the output pulse‐height spectra until ultimately the 59.5‐keV photopeak of the241Am gamma ray can not be discerned. Following annealing at 600 K, the pulse‐height spectrum recovers almost to the preirradiation value. This annealing behavior coincides with the recovery of the electron‐drift mobility of bulk crystals.