Plasma flow control is a novel active flow control method using plasma aerodynamic actuation and has advantages of high strength, fast response, and broad bandwidth. Its origin dates back to the 1960s, with significant development from the 1990s onward. Various discharge methods, such as dielectric-barrier discharge and arc discharge, are used to generate plasma aerodynamic actuation. The main effects of plasma aerodynamic actuation include momentum effect, shock effect, and chemical effect. For separation control, a new principle named plasma shock flow control is put forward and validated for airfoil separation control at high subsonic conditions. For shock wave control, controlled experiments and modeling converge to the mechanism that heating effect is global in many cases, while ionization effect is less important. For further development, shock/boundary layer interaction control and transition delay are two important contents.