Cadmium telluride (CdTe) and cadmium zinc telluride (CdZnTe) have been regarded as promising semiconductor materials for hard X-ray and γ-ray detection. The high atomic number of the materials (Z Cd =48, Z T e =52) gives a high quantum efficiency in comparison with Si. The large band-gap energy (Eg ∼ 1.5 eV) allows us to operate the detector at room temperature. However, a considerable amount of charge loss in these detectors produces a reduced energy resolution. This problem arises due to the low mobility and short lifetime of holes. Recently, significant improvements have been achieved to improve the spectral properties based on the advances in the production of crystals and in the design of electrodes. In this overview talk, we summarize (1) advantages and disadvantages of CdTe and CdZnTe semiconductor detectors and (2) technique for improving energy resolution and photopeak efficiencies. Applications of these imaging detectors in future hard X-ray and gamma-ray astronomy missions are briefly discussed.