With the development of the modern manufacturing industry, especially that of high-speed and high-precision machining, higher performances of computer numerical control (CNC) machine tools are necessary than ever. For high-precision CNC machine tools, vibration in high-speed machining is an important factor to affect the machining accuracy. As a significant part of CNC machine tools, the dynamic characteristics of the feed drive system have a great impact on the machining performance. Ball screw drive systems are widely applied in the majority of CNC machine tools for the time being. In the process of high-speed machining, the vibration of the ball-screw drive system will affect the stability of the control system and the machining accuracy of CNC machine tools. Thus, further investigation of dynamic characteristics and vibration control methods of the ball-screw drive system will be of great importance to improve the machining performance. A comprehensive review is carried out here to research statuses of vibration analysis and control methods for feed drive systems. Related studies on system modeling, parameter identification, and vibration control technologies are classified and summarized. The advantages and disadvantages of different methods are discussed and compared. Moreover, the linear parameter-varying (LPV) modeling method of ball-screw drive systems and corresponding control technologies are introduced in detail. Finally, related research prospects are systematically presented based on the existing studies, and these research directions which are rarely studied will be of great significance to develop vibration control technologies for CNC machine tool feed drive systems.