We present laboratory results from our compound semiconductor program designed to produce X- and gamma-ray detectors with both high spectral and spatial resolution and with high quantum efficiencies over the energy range 1 to 500 keV. A number of materials are presently under study, including GaAs, InP, CdZnTe, HgI2 and TlBr. Extensive measurements on simple monolithic detectors and small format arrays have been carried out both in our laboratory and at the ESRF, HASYLAB and BESSY II synchrotron radiation facilities. The results have been used in conjunction with a material science program ultimately intended to produce near Fano limited, monolithic detectors and large area pixelated arrays for the next generation X-ray astrophysics and planetary space missions.