The attacks and defenses on the information of which website pages are visited by users are important research subjects in the field of privacy enhancing technologies, they are termed as website fingerprinting (WF) attacks and defenses. Nowadays, deep learning is an important tool in many research areas, including WF attacks and defenses. In this paper, we offer a comprehensive survey on deep learning for WF attacks and defenses. After a brief introduction, we first summarize deep learning, WF attacks, and WF defenses. For deep learning, we review the common paradigms, architectures, and performance metrics. For WF attacks, we review the approaches, challenges and solutions. The approaches include deep learning, traditional machine learning, and other methods. Challenges and solutions cover multi-tab browsing, concept drift, and the base rate fallacy. For WF defenses, we review the strategies and approaches. Then, we survey deep learning for WF attacks, and deep learning for WF defenses. In deep learning for WF attacks, we survey in detail the deep learning paradigms, architectures of WF attack models, and the performance of several representative WF attack models, and look into the future. In deep learning for WF defenses, we survey the architecture, efficacy and overhead of deep learning models in WF defenses, and look into the future. In the end, we summarize this paper.