The paper presents an analysis of the current state of the art in the control of aero- or hydrodynamic instabilities in turbomachines. It describes the flow phenomena associated with rotating stall and surge, discusses methods devised to prevent these instabilities occuring, but concentrates mainly on the active control (stabilization) of the unstable flows. It appears that lately significant progress has been made in this area. It seems to foster to a more mature state, although several problems deserve further consideration. The consequences of this state of the art for several interested parties, researchers, developers, manufacturers, and users, are stipulated