Compared to 2D display, 3D display presents information with more realistic visual perceptions. It is a vital technology in the fields of 5G, metaverse, big data and internet of things. 3D display based on computer-generated holography can provide various kinds of depth cues. It presents an outstanding 3D effect and is considered as an ultimate form of 3D display. It is believed that holographic 3D display would have broad application prospects in intelligent manufacturing, distance education, telecommuting, entertainment and social networking. In this review, the history and important technical nodes of computer-generated holography were introduced. According to the current status of the technology, main challenges faced by high-quality dynamic holographic 3D display were introduced, including limited accuracy of computer-generated hologram, imperfect performance of wavefront modulator and holographic display system, and shortage of 3D content. Focusing on these challenges, the existing solutions were summarized. Advantages and disadvantages of various solutions were compared. Research directions of high-quality dynamic holographic 3D display were analyzed, including low-noise holographic algorithms, distortion calibration methods, and 3D content generation technologies. Holographic 3D display with low noise, high refresh rate and high precision, which were inevitable in some applications such as meteverse, could be realized by addressing these issues.