With the advent of the fourth industrial revolution, data-driven decision making has also become an integral part of decision making. At the same time, deep learning is one of the core technologies of the fourth industrial revolution that have become vital in decision making. However, in the era of epidemics and big data, the volume of data has increased dramatically while the sources have become progressively more complex, making data distribution highly susceptible to change. These situations can easily lead to concept drift, which directly affects the effectiveness of prediction models. How to cope with such complex situations and make timely and accurate decisions from multiple perspectives is a challenging research issue. To address this challenge, we summarize concept drift adaptation methods under the deep learning framework, which is beneficial to help decision makers make better decisions and analyze the causes of concept drift. First, we provide an overall introduction to concept drift, including the definition, causes, types, and process of concept drift adaptation methods under the deep learning framework. Second, we summarize concept drift adaptation methods in terms of discriminative learning, generative learning, hybrid learning, and others. For each aspect, we elaborate on the update modes, detection modes, and adaptation drift types of concept drift adaptation methods. In addition, we briefly describe the characteristics and application fields of deep learning algorithms using concept drift adaptation methods. Finally, we summarize common datasets and evaluation metrics and present future directions.