Nonlinear microwave device modeling is an important part of computer-aided design (CAD) and many papers have been published in the literature. This paper presents a review of neural network based techniques for nonlinear microwave device modeling including recurrent neural network (RNN), neuro-space mapping (Neuro-SM) and dynamic Neuro-SM techniques. Large-signal waveforms or DC, small-signal and large-signal harmonic data are used as training data. Compared with conventional equivalent circuit models, the models generated by these neural network based methods are more accurate and more efficient to represent the behavior of the device.