The deregulation of the power industry requires avoiding market power abuse to maintain the market competitiveness. To this end, a sequence of assessment measurements or mitigation mechanisms is required. Meanwhile, the increasing renewable energy resources (RESs) and flexible demand response resources (DRSs) are changing the behaviors of market participants and creating new cases of market power abuse. Such new circumstances bring the new evaluation and control methods of market power to the forefront. This paper provides a comprehensive review of market power in the reshaping of power systems due to the increasing RES and the development of DRS. The market power at the supply side, demand side, and in the multi-energy system is categorized and reviewed. In addition, the applications of market power supervision measures in the US, the Nordics, UK, and China are summarized. Furthermore, the unsolved issues, possible key technologies, and potential research topics on market power are discussed.