The objective of this paper is to provide a succinct review of past and current research in developing wave rotor technology. This technology has shown unique capabilities to enhance the performance and operating characteristics of a variety of engines and machinery utilizing thermodynamic cycles. Although there have been a variety of applications in the past, this technology is not yet widely used and is barely known to engineers. Here, an attempt is made to summarize both the previously reported work in the literature and ongoing efforts around the world. The paper covers a wide range of wave rotor applications including the early attempts to use wave rotors, its successful commercialization as superchargers for car engines, research on gas turbine topping, and other developments. The review also pays close attention to more recent efforts: utilization of such devices in pressure-gain combustors, ultra-micro gas turbines, and water refrigeration systems, highlighting possible further efforts on this topic. Observations and lessons learnt from experimental studies, numerical simulations, analytical approaches, and other design and analysis tools are presented.