Gas foil bearings have important and wide applications in high-speed turbomachinery, generating low frictional lubricating gas film in series with underlying elastic foil structures to support the rotor system. Their dynamic performance is of vital significance in maintaining the rotor stability as well as in depressing rotor vibrations. This paper conducts a comprehensive review on dynamic performance studies conducted on gas foil bearings, including research on the dynamic stiffness and damping coefficients, bearing stability, nonlinear vibrations of the rotor–bearing system, and active methods for controlling rotor dynamic motions. This review provides clear observations towards the developments and iterations of the models, methods, and experiments of these studies.