Abstract: Flexible manipulators usually have flexible joints ard/or links. Over the last four decades, research on flexible manipulators has greatly progressed. In this paper, the development status, research hotspots, and frontier progress of flexible manipulators in dynamic modeling methods, vibration sensor measurement systems, and control algorithms are reviewed. Firstly, the advantages, disadvantages, and complexities of flexible manipulators are briefly explained, and the modeling methods and technologies of flexible joints and flexible manipulator robots are introduced. Secondly, the application and characteristics of different vibration measurement systems in flexible manipulators are described. The advantages and disadvantages of different measurement methods in the vibration measurement of flexible manipulators are compared. Then, the vibration control methods and control algorithms of flexible manipulators proposed in various studies are emphatically reviewed. The research status of the self-excited vibration and control of flexible parallel manipulators is also analyzed. Lastly, the development trend, problems, and challenges of future research work are discussed.