Abstract: Flux-fluctuation law means the scaling relationship between the mean and the stand errors of traffic in networks. This law has been observed in a wide range of complex systems. Understanding the origin of flux-fluctuation law is fundamental and significant to the dynamics of complex systems. This review article summarizes the state-of-the-art progresses of flux-fluctuation law in complex systems, and give a detailed description of typical models and major results in this area. Moreover, we propose an easy mathematical model, with which we use the mathematic language to provide a universal framework for previous major models. Furthermore, this article reviews the advanced and insufficient points of related works, and points out some unsolved challenges in both theoretical and practical aspects.