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This article presents the operating physics, performance potential, and status of device development of microwave AlGaN/GaN heterostructure field-effect transistors. AlGaN/GaN HFETs show potential for use in improved RF performance microwave amplifier applications. Development progress has been rapid, and prototype devices have demonstrated RF output power density as high as 30 W/mm. Microwave amplifier output power is rapidly approaching 100 W for single-chip operation, and these devices may soon find application for cellular base station transmitter applications. Devices are being developed for use in X-band radars, and RF performance is rapidly improving. The HFET devices experience several physical effects that can limit performance. These effects consist of nonlinearities introduced during the high-current and high-voltage portions of the RF cycle. High-current phenomena involve the operation of the conducting channel above the critical current density for initiation of space-charge effects. The source resistance is modulated in magnitude by the channel current, and high source resistance results. High voltage effects include reverse leakage of the gate electrode and subsequent charge trapping effects on the semiconductor surface, and RF breakdown in the conducting channel. These effects can produce premature saturation effects. Also, under certain conditions, high voltage operation of the device can initiate an IMPATT mode of operation. When this occurs, the channel current increases and RF gain is increased. This phenomenon enhances the RF output power of the device. The physical limiting effects can be controlled with proper design, and the outlook for use of these devices in practical applications is excellent.