The semiconductor silicon is the dominant material in microelectronics and is one of the best-studied materials known to humanity. Its inability to emit light efficiently is therefore well documented. Nevertheless, a “holy grail” of semiconductor materials research has for decades been the realization of an efficient Si light-emitting diode (LED). Such a device would enable optoelectronic circuitry to be based entirely on silicon and would revolutionize VLSI technology since the other required Si-based devices (detectors, waveguides, modulators, etc.) have already been demonstrated. Although this holy grail has proved elusive, the 1990s have heralded greatly renewed interest and optimism in the development of such devices for both the visible and near-infrared spectral ranges. Dramatic progress is at last being made. This review focuses, in a somewhat chronological manner, on the progress of specific approaches to realizing crystalline structures of high radiative efficiency, and the materials constraints involved.