In this review article, the growth and related academic communications in the dynamics of multibody systems are firstly surveyed. Then, the recent advances in the numerical algorithms for solving the dynamic equations of flexible multibody systems, the contact/impact dynamics of flexible multibody systems and the deployment of flexible space structures are systematically reviewed, together with several open problems of concern. Finally, some suggestions are made for the prospective researches on the dynamics of flexible multibody systems.