Abstract: Information gap decision theory（IGDT） is a method using non-probabilistic model to deal with the "Knightian uncertainty" caused by factors such as electricity price, output and load in the current power system. This method has been applied to many optimization fields such as power system which needs to deal with uncertainty. The basic theory, optimization model and decision preference model of IGDT have been introduced in this paper. The application of IGDT in power system is summarized from three aspects: system planning, system operation and power market. According to the scale of the network, the power system has been divided into micro network, distribution network and power grid, and the operation of the system has been discussed. According to the perspective of market participants, the power system can be divided into four categories: generator, retailer, large user and operator, and the relevant work of the power market has been compared. Finally, the application of IGDT in power system is summarized in order to achieve the purpose that IGDT can be more widely used.