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Semiconductors provide some of the most promising materials for nonlinear optics, because of large resonant nonlinearities, control of recombination time (from milliseconds to femtoseconds), well-developed fabrication technologies, and compatibility with other optoelectronic devices. The paper reviews some of the concepts and results that have come from the study of nonlinear optics in semiconductors. The emphasis is on nonlinear absorption and the refractive index that arises from the photo-induced excitation of free carriers. Mechanisms described include state-filling, carrier transport, and photorefractivity. Devices include optical bistability, reflective asymmetric Fabry-Perot all-optical absorptive switches, optically addressed spatial light modulators, and real-time holography. The paper's approach is to provide a basic engineering understanding of the principles, some of the historical details, and a snapshot of the state of the field today.