The current status of Schottky CdTe diode detectors, especially in view of their space application for hard X-ray and gamma-ray astronomy, are reported. For practical use in space science, a large-area CdTe diode with a size of 21.5×21.5mm2 and a thickness of 0.5mm was developed. A good energy resolution, 2.8keV (FWHM) at -20°C, and high homogeneity to within 0.2% over the detector were achieved for the spectral performance. This device has successfully passed a series of tests required for its use in space, in view of utilizing Japanese M-V rockets. The tests include the mechanical environment test, vacuum test, long run for weeks and proton-beam radiation. Initial results from a 2×2 segmented electrode large-area device with a guard-ring are also presented.