This review studies some of the existing ideas which create a fundamentally new direction for wave energy converter (WEC) development, obtaining energy from the elliptical motion of particles in water waves using a rotor. The review focuses on three main aspects of rotor-based WECs: experimental study of the developed prototypes, derivation and development of the mathematical models, and control effectors and philosophies for the proposed devices. The range of developed small scale prototypes and their experimental studies are presented. The shortcomings of the current mathematical and hydrodynamic models are identified, while an overview of the proposed and new possible control effectors and strategies is conducted. This allows us to see the state of the development of the different concepts and problems to be solved in bringing wave energy rotors to operational reality.