With the development of the intelligent information era, applications of deep neural networks in various fields of human society, especially deployments in safety-critical systems such as automatic driving and military defense, have aroused concern from academic and industrial communities on the erroneous behaviors that deep neural networks may exhibit. Although neural network verification and neural network testing can provide qualitative or quantitative conclusions about erroneous behaviors, such post-analysis cannot prevent their occurrence. How to repair the pre-trained neural networks that feature wrong behavior is still a very challenging problem. To this end, deep neural network repair comes into being, aiming at eliminating the unexpected predictions generated by defective neural networks and making the neural networks meet certain specification properties. So far, there are three typical neural network repair paradigms: retraining, fine tuning without fault localization, and fine tuning with fault localization. This study introduces the development of deep neural networks and the necessity of deep neural network repair, clarifies some similar concepts, and identifies the challenges of deep neural network repair. In addition, it investigates the existing neural network repair strategies in detail and compares the internal relationships and differences among these strategies. Moreover, the study explores and sorts out the evaluation metrics and benchmark tests commonly used in neural network repair strategies. Finally, it forecasts the feasible research directions that should be paid attention to in the future development of neural network repair strategies.