The rapid development of computer technology has promoted the research of complex network synchronization in network environments, which involves practical fields such as the Internet of Things, transportation networks, social networks, and biological systems. In this paper, the latest research and trends in limited bandwidth complex network synchronization control are surveyed. The following aspects are discussed regarding control methods for complex network synchronization and limited communication bandwidth: Firstly, by analyzing current research on complex network control, the methods of discontinuous control and finite-time control are discussed. Secondly, from the perspective of effectively utilizing communication bandwidth resources, synchronization control methods for complex networks with limited bandwidth are described. On the one hand, the studies on event-triggered synchronization control for complex networks are reviewed to reduce the volume of data transmissions. On the other hand, research on synchronization control in complex networks using quantification-based coding-decoding methods is explored to reduce the volume of transmitted data. In addition, considering the current security issues facing networks and systems, the ongoing research on secure synchronization control of complex networks under cyber-attacks is described. Lastly, some future directions for investigating the synchronization of complex networks with limited bandwidth are suggested.