The fission behavior of flocking system is the splitting phenomenon of a cohesive flock into multiple subgroups, investigation on the internal mechanisms and control methods of such behavior is of both theoretical significance and practical value. Therefore, the state-of-the-art of fission behavior for flocking system is overviewed from two aspects, the theoretical models and fission control methods. In particular, the latest development of the theoretical models for fission behavior is reviewed. Meanwhile, the research results on fission control are summarized and the problems that remain un