Stable operation of both axial and radial compressors is constrained by rotating stall and surge. Developments in the understanding of the physics behind these instabilities, and ideas of how to stabilize the compressor system, have opened the door to a new era in the field of compressor control: so-called active control. The paper gives an overview of the current state of modeling and control of aerodynamic flow instabilities in axial and radial compressors. It discusses the differences between rotating stall and these compressors but focuses on active control systems applied in experimental studies. The evolution of models and control systems demonstrates that this research area is still developing, but models cannot yet describe all form...