Motion system is the core subsystem of integrated circuit (IC) manufacturing equipment for achieving high-speed, high-precision, and strong stability. With increasing performance and production efficiency requirements of IC manufacturing, the motion system of IC manufacturing equipment should have extremely high precision, high response speed, as well as strong excellent robustness and stability. However, its dynamic modeling and control was seriously challenged by the multi-degree-of-freedom and rigid-flexible coupling characteristics, nonlinear and time-varying dynamic characteristics, measurement noise, and parameter uncertainty. The linear parameter-varying (LPV) theory provides a new solution approach to the above problems, this paper briefly surveys the motion system of IC manufacturing equipment and its modeling and control problems. Secondly, it reviews the LPV modeling and control methods of the motion system of IC manufacturing equipment from the three aspects of modeling, identification, and control. Finally, it summarizes and prospects the research on dynamic modeling and control of IC manufacturing equipment motion system.