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Machine learning (ML) has been widely applied to the upper layers of wireless communication systems for various purposes, such as deployment of cognitive radio and communication network. However, its application to the physical layer is hampered by sophisticated channel environments and limited learning ability of conventional ML algorithms. Deep learning (DL) has been recently applied for many fields, such as computer vision and natural language processing, given its expressive capacity and convenient optimization capability. The potential application of DL to the physical layer has also been increasingly recognized because of the new features for future communications, such as complex scenarios with unknown channel models, high speed and accurate processing requirements; these features challenge conventional communication theories. This paper presents a comprehensive overview of the emerging studies on DL-based physical layer processing, including leveraging DL to redesign a module of the conventional communication system (for modulation recognition, channel decoding, and detection) and replace the communication system with a radically new architecture based on an autoencoder. These DL-based methods show promising performance improvements but have certain limitations, such as lack of solid analytical tools and use of architectures that are specifically designed for communication and implementation research, thereby motivating future research in this field.