With the increasingly powerful performance of neural network models, they are widely used to solve various computer-related tasks and show excellent capabilities. However, a clear understanding of the operation mechanism of neural network models is lacking. Therefore, this study reviews and summarizes the current research on the interpretability of neural networks. A detailed discussion is rendered on the definition, necessity, classification, and evaluation of research on model interpretability. With the emphasis on the focus of interpretable algorithms, a new classification method for the interpretable algorithms of neural networks is proposed, which provides a novel perspective for the understanding of neural networks. According to the proposed method, this study sorts out the current interpretable methods for convolutional neural networks and comparatively analyzes the characteristics of interpretable algorithms falling within different categories. Moreover, it introduces the evaluation principles and methods of common interpretable algorithms and expounds on the research directions and applications of interpretable neural networks. Finally, the problems confronted in this regard are discussed, and possible solutions to these problems are given.