Channel coding (error correction coding) is the basis of ensuring the reliable communication. Polar code is the first constructive coding method which can achieve the channel capacity. It has practical linear encoding and decoding complexity and excellent error correction and detection performance. The unique advantages of polar codes make it have a broad application prospect in the communication systems such as next-generation mobile communication systems, satellite communications, deep space exploration. In recent years, with the application of polar codes in the fifth-generation mobile communication standards and systems, the theory and application of polar codes are changing with each passing day. In this paper, several hot issues in the research of polar codes are summarized, and the future research of polar codes are discussed.