Dynamics research and control of high-speedmechanisms, which may involve many fields of developing subjects, are a tough problem. The advances in the fieldsof flexible multibody dynamics and time-periodic systems, which are the bases of dynamics research in the fields of high-speed mechanisms, are surveyed at first. Then, the state-of-arts of the dynamics research in some typical mechanisms such as linkage mechanisms and cam-follower mechanisms is introduced in detail. The research on the dynamics of mechanisms with clearances is followed with interest and the advances of active vibration control in flexible mechanisms are briefly dealt with. Finally, a number of open problems in the fields concerned areaddressed.