The asymmetric operation is a method that allows High and Extra-High Voltage (HV, EHV) power lines to function with one or two phases open. With the increasing share of Renewable Energy Sources (RES) in National Power Systems (NPS), they are becoming more volatile and less reliable due to decreasing inertia and other issues related to the integration and exploitation of the Inverter-Based Resources (IBR) (decreasing short-circuit ratio, different types of interactions, etc.). On the other hand, phase-to-ground faults are a common cause of tripping off power lines which affects the overall reliability of the power system. Thus, for power systems experiencing a decreasing trend in reliability and robustness, the asymmetrical operation of the power lines may enhance them. In this way, this article reviews the state of the art and new developments in the academic landscape regarding asymmetrical operation. The review is not, however, limited to HV and EHV systems, so it examines cases of asymmetric operation in Low and Medium Voltages (LV, MV) as well. The challenges and opportunities that this unique mode of operation imposes on power networks are also presented, providing a fresh reference for researchers looking to enter this topic.