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Echo state network (ESN) is a new type of recurrent neural network (RNN) proposed in recent years. The training process of ESN is easier and requires less computational effort than regular RNN which has the same size. Due to its high modeling capability of complex dynamic system, ESN has been used in various power system applications such as power system nonlinear load modeling and true harmonic current detection, wide area monitoring, intelligent control of an active power filter (APF), overhead conductor thermal dynamics identification, wind speed or water inflow forecasting, etc. This paper introduces the basic concept and the offline and online training algorithms of the ESN in detail and reviews the state of the art of ESN applications in power systems.