The recent development of deep learning methods demonstrates a new insight to optimize the decoding of linear codes. In this paper, we survey the typical neural network decoding methods, including data-driven and model-driven schemes. We investigate the design principle, algorithm mechanism, parameter assignment, and training process of these neural decoders for high-density parity check (HDPC), low-density paritycheck (LDPC), and polar codes. Finally, we summarize the advantages of neural network decoding and point out some research directions in the future.