Reconfigurable intelligent surface (RIS) has recently emerged as a promising paradigm for future cellular networks. Specifically, due to its capability in reshaping the propagation environment, RIS was introduced to address the blockage issue in millimeter Wave (mmWave) or even Terahertz (THz) communications. The deployment of RIS, however, complicates the system architecture and poses a significant challenge for beam training (BT)/ beam alignment (BA), a process that is required to establish a reliable link between the transmitter and the receiver. In this article, we first review several state-of-the-art beam training solutions for RIS-assisted mmWave systems and discuss their respective advantages and limitations. We also present a new multi-directional BT method, which can achieve a decent BA performance with only a small amount of training overhead. Finally, we outline several important open issues in BT for RIS-assisted mmWave systems.