As the number of electric vehicles (EV) continues to grow, large-scale uncontrolled charging of electric vehicles will have a huge impact on the power grid and the transport network. The use of EVs, with their spatial and temporal flexibility and mobile energy storage characteristics, can ensure the smooth operation of power grids and transportation networks by guiding the orderly charging of EVs. This paper begins with an introduction to the various aspects involved in electric vehicle demand response. It compares the research related to EV optimal dispatching from the perspective of dispatching means, and introduces two dispatching means, including price-based demand response and incentive-based demand response. And then, it introduces the research on the application of EVs on the grid and transportation network in detail, and summarizes and concludes. It analyzes the shortcomings of the existing research and gives an outlook on further research in the future.