Communication in millimeter wave (mmWave) and even terahertz (THz) frequency bands is ushering in a new era of wireless communications. Beam management, namely initial access and beam tracking, has been recognized as an essential technique to ensure robust mmWave/THz communications, especially for mobile scenarios. However, narrow beams at higher carrier frequency lead to huge beam measurement overhead, which has a negative impact on beam acquisition and tracking. In addition, the beam management process is further complicated by the fluctuation of mmWave/THz channels, the random movement patterns of users, and the dynamic changes in the environment. For mmWave and THz communications toward 6G, we have witnessed a substantial increase in research and industrial attention on artificial intelligence (AI), reconfigurable intelligent surface (RIS), and integrated sensing and communications (ISAC). The introduction of these enabling technologies presents both open opportunities and unique challenges for beam management. In this paper, we present a comprehensive survey on mmWave and THz beam management. Further, we give some insights on technical challenges and future research directions in this promising area.