With the rapid development of wireless communication technology, intelligent communication has become one of the mainstream research directions after the fifth generation (5G). In particular, deep learning has emerged as a significant artificial intelligence technology widely applied in the physical layer of wireless communication for achieving intelligent receiving processing. Channel estimation, a crucial component of physical layer communication, is essential for further information recovery. As a motivation, this paper aims to review the relevant research on applying deep learning methods in channel estimation. Firstly, this paper briefly introduces the conventional channel estimation methods and then analyzes their respective merits and drawbacks. Subsequently, this paper introduces several common types of neural networks and describes the application of deep learning in channel estimation according to data-driven and model-driven approaches, respectively. Then, this paper extends to emerging communication scenarios and discusses the existing research on channel estimation based on deep learning for reconfigurable intelligent surface (RIS)-aided communication systems. Finally, to meet the demands of next-generation wireless communication, challenges and future research trends in deep-learning-based channel estimation are discussed.