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Demand response (DR) is the outreach of demand side management (DSM) in competitive electricity markets. With price signals and incentive mechanisms, DR is crucial to both power system reliability and market efficiency. Based on DR research and experiences around the world, comprehensive research on DR in electricity markets is conducted, including its definition, classification, implementation mechanisms, impacts on power systems, and cost-benefit analysis. According to different reasons for triggering DR, DR programs in electricity markets are classified into two categories: price-based DR and incentive-based DR. Subsequently, for each category, this paper discusses several representative DR programs to shed detailed light on two key problems, i.e., DR implementation mechanisms and the impacts of DR on power systems. Several important problems which need to be further studied are finally proposed.