For some decades, efforts have been made to exploit nonsteady combustion and gas dynamic phenomenon. The theoretical potential of nonsteady-flow machines has led to the investigation of various oscillatory flow devices such as pulse detonation engines, wave rotors, pulse jets, and nonsteady ejectors. This paper aims to provide a progress review of past and current research in developing a particular combustion concept: the wave rotor combustor. This pressure-gain combustor appears to have considerable potential to enhance the performance and operating characteristics of gas turbine and jet engines. After attempts in the mid-twentieth century were thwarted by mechanical problems and technical challenges identified herein, recent successes in Switzerland and efforts in the United States benefited from design expertise developed with pressure-exchange wave rotors. The history, potential benefits, past setbacks, and existing challenges and obstacles in developing these nonsteady combustors are reviewed. This review focuses on recent efforts that seek to improve the performance and costs of future propulsion and powergeneration systems.