The research on complex systems is different from that on general systems because the former must consider self-organization, emergence, uncertainty, predetermination, and evolution. As an important method to transform the world, a simulation is one of the most important skills to discover complex systems. In this study, we provide a survey on complex systems and their simulation methods. Initially, the development history of complex system research is summarized from two main lines. Then, the eight common characteristics of the most complex systems are presented. Furthermore, the simulation methods of complex systems are introduced in detail from four aspects, namely, meta-synthesis methods, complex networks, intelligent technologies, and other methods. From the overall point of view, intelligent technologies are the driving force, and complex networks are the advanced structure. Meta-synthesis methods are the integration strategy, and other methods are the supplements. In addition, we show three complex system simulation examples: digital reactor simulation, simulation of a logistics system in the industrial site, and crowd evacuation simulation. The examples show that a simulation is a useful means and an important method in complex system research. Finally, the future development prospects for complex systems and their simulation methods are suggested.