Reasonable control of charging and discharging for electric vehicles（EVs）can improve the safety and economy of electric power system, and significantly reduce charging costs for EV users. The demand response strategy is one of the key technologies for orderly charging and discharging of EVs, which can solve a serious of problems caused by large-scale EVs interfacing with the grid and improve the consumption ratio of renewable energy in the grid. It has been widely studied by scholars at home and abroad.Firstly, the background and technology of demand response are illustrated. Then, aiming at the characteristics of demand response,the price-based and incentive-based demand response strategies are analyzed and compared respectively. Finally, relative suggestions are put forward for the domestic development of demand response for charging and discharging of EVs.