A lithography machine is a key equipment to support the continuous reduction of the size of the integrated circuit. High-performance lithography machine requires high-acceleration and high-precision motion stages. To meet the requirements of the lithography machine, high-performance stage control methods are essential. This paper sorts out and introduces the mainstream control methods of motion stages in the lithography machine. First, the working principle and basic control structure of motion stages are introduced. Then, the control methods of the motion stage are introduced in detail from the aspects of feedforward control, feedback control and over-actuation/over-sensing, to provide a reference for the further development of control methods of lithography machine motion stages.