Deregulation of the power industry requires avoiding market power abuse for maintaining market competitiveness. To this end, a sequence of assessment measurements or mitigation mechanisms is required. Meanwhile, the increasing renewable energy sources (RES) and flexible demand response resources (DRS) are changing the behaviors of market participants and creating new cases of market power abuse. Such new circumstances brought the brand-new evaluation and control methods of market power to the forefront. This paper presents a comprehensive review of market power in the reshaping of power systems brought by RES and DRS. The market power in the supply side, the demand side and in the multi-energy system are categorized and reviewed. Besides, the application of market power supervision measures in the US, Nordic, UK and China is summarized. Furthermore, the unsolved issues, possible key technologies, and potential research topics on market power are discussed. This paper may provide references and new perspectives for the upcoming research in market power under various environments.