This paper reviews the application of recurrent neural net-work (RNN) in electromagnetic and microwave fields. One is based on long- and short-term memory (LSTM) neural network, the forward model of time domain electromagnetic field (TDEM) is studied, and the other is to use RNN to model the behavior of power amplifier (PA) with memory effect. Firstly, in order to solve the electromagnetic scattering problem, the long short-term memory time domain electromagnetic (LSTM-TDEM) model is adopted. Its effective-ness is verified by training and experiment. Secondly, the modeling of PA behavior utilizes the long-term and short-term memory effect of RNN, and the model can better reflect the nonlinear characteristics of the system.