Argumentation systems are a kind of non-monotonic formalisms, capable of supporting the reasoning and decision-making of individual agents, and the effective interactions among multiple agents. Since the knowledge, observations of an individual agent and the interacting process of different agents are dynamic in various argumentation systems, the changing of arguments and attacks is pervasive. As a new research area, the concepts, theories and methods related to dynamic of argumentation systems are far from mature. After introducing the basic working mechanism of argumentation systems, this paper presents two research directions of dynamics of argumentation systems (i.e., forward dynamics and backward dynamics) and discusses some open problems to be resolved. According to these problems, the paper briefly reviews the existing theories and methods, and analyzes their properties and shortcomings.