Abstract: There have been alarge number of studies recently on space inflatable structures,which can offer extremely low weight, inherent low launch volumeand on-orbit deployment reliability in many large deployablespacecraft applications. Some space programs taking advantages of inflatable structures have been suggested already.However, some important problems must be solved before inflatablestructures can be applied in space environment. One such problemconcerns the control and the deployment dynamics properties of thestructure throughout the inflation and deployment process. Theinflatable boom to deploy and support space structures is a keycomponent of many space inflatable structures. In view of theirimportance, the progress of deployment dynamics of inflatablebooms during the past twenty years is summarized. Several kinds ofinflatable deployment models are discussed, including thenonlinear hinge model, the deployment model of rolled booms, thecontrol volume model, the conservation model of energy andmomentum, and the fluid-structure interaction model. Then, thesimulations using finite element method are discussed. Inflatabledeployment experiments for Z-folded, rolled, polygon andtelescopic conical booms are then reviewed. At the end of thepaper, some attractive topics for further research on thedeployment dynamics of inflatable booms are suggested, includingtheoretical studies, numerical simulations and experimentalstudies.