Compressors are widely used for the pressurization of fluids. Applications involve air compression for use in aircraft engines and pressurization and transportation of gas in the process and chemical industries. The article focuses on two commonly used types of continuous flow compressors: the axial compressor, where the gaseous fluid is processed in a direction parallel to the rotational axis, and the radial or centrifugal compressor, where the pressurized fluid leaves the compressor in a direction perpendicular to the rotational axis. In these machines, the entering fluid is pressurized by first accelerating it via the kinetic energy imparted in the rotors and then converting the kinetic energy into potential energy by decelerating the fluid in diverging channels. Toward low mass flows, stable operation of axial and radial compressors is constrained by two aerodynamic flow instabilities: rotating stall and surge. The article gives an overview of the current state of modeling and control of these instabilities.