The research on the interpretability of deep learning is closely related to various disciplines such as artificial intelligence, machine learning, logic and cognitive psychology. It has important theoretical research significance and practical application value in too many fields, such as information push, medical research, finance, and information security. In the past few years, there were a lot of well studied work in this field, but we are still facing various issues. In this paper, we clearly review the history of deep learning interpretability research and related work. Firstly, we introduce the history of interpretable deep learning from following three aspects: origin of interpretable deep learning, research exploration stage and model construction stage. Then, the research situation is presented from three aspects, namely visual analysis, robust perturbation analysis and sensitivity analysis. The research on the construction of interpretable deep learning model is introduced following four aspects: model agent, logical reasoning, network node association analysis and traditional machine learning model. Moreover, the limitations of current research are analyzed and discussed in this paper. At last, we list the typical applications of the interpretable deep learning and forecast the possible future research directions of this field along with reasonable and suitable suggestions.