Gallium-nitride power transistor (GaN HEMT) and integrated circuit technologies have matured dramatically over the last few years, and many hundreds of thousands of devices have been manufactured and fielded in applications ranging from pulsed radars and counter-IED jammers to CATV modules and fourth-generation infrastructure base-stations. GaN HEMT devices, exhibiting high power densities coupled with high breakdown voltages, have opened up the possibilities for highly efficient power amplifiers (PAs) exploiting the principles of waveform engineered designs. This paper summarizes the unique advantages of GaN HEMTs compared to other power transistor technologies, with examples of where such features have been exploited. Since RF power densities of GaN HEMTs are many times higher than other technologies, much attention has also been given to thermal management-examples of both commercial "off-the-shelf" packaging as well as custom heat-sinks are described. The very desirable feature of having accurate large-signal models for both discrete transistors and monolithic microwave integrated circuit foundry are emphasized with a number of circuit design examples. GaN HEMT technology has been a major enabler for both very broadband high-PAs and very high-efficiency designs. This paper describes examples of broadband amplifiers, as well as several of the main areas of high-efficiency amplifier design-notably Class-D, Class-E, Class-F, and Class-J approaches, Doherty PAs, envelope-tracking techniques, and Chireix outphasing.