The drag-free control of the spacecraft is one of the key technologies to realize the ultra-static and ultra-stable operation of science platform for gravitational wave space detection. At present, the dynamics and control of the spacecraft system have been studied deeply by various research institutions at domestic and overseas, and different detection tasks have been proposed according to the requirements of different detection frequency bands. The design and control of spacecraft formation were introduced and analyzed in detail according to the exploration mission, and the principles and theoretical methods of drag-free and attitude control, high-precision inertial sensors and actuators involved were deeply dissected. The overall situation of demonstration and verification of drag-free spacecraft in orbit for space-based gravitational wave detection was detailed and analyzed. On this basis, the key problems required to be solved in the research of follow-up related were presented, and the research hotspots and trends in the methods of future dynamics and control of drag-free spacecraft systems were also pointed out.