The focus of this article is the pressure-control problem of gas generators employed in variable-speed rockets. The ability to change the speed during operation enables these rockets to adjust to the demands of different types of maneuvers and varying flight conditions. As a result, speed-controllable rockets provide a dramatic advantage over their alternatives with fixed speed profiles. In throttleable ducted rockets, speed variation is achieved by changing the fuel flow rate (throttleability), which requires a careful controller design. The article provides a detailed review of the current state of rocket propulsion control and the main challenges in the field. A controller (which contains a unique combination of traits such as fast adaptation, delay compensation, and provision of a smooth response) is introduced as a solution to the pressure control problem in air-breathing rocket propulsion. The superior performance of the controller, compared to existing alternatives, is demonstrated through experimental tests, using a test setup provided by Roketsan, Inc.