Abstract: The spacecraft formation flying is defined as the tracking or the maintenance of a desired relative separation, orientation or position between or among several spacecraft. This paper reviews the dynamics and the control of the spacecraft formation flying in Earth orbit, including the modelling methods and the control design techniques of the conventional propulsion system and the novel propellant-less system. The conventional propulsion system, where the spacecraft is actuated by thrusters using chemical fuels or plasma, can achieve a high accuracy and variable formation constellations with a relatively large power consumption. By contrast, the novel propellant-less system, where the spacecraft is actuated by novel means of actuation such as the atmospheric drag effect, the non-contacting internal forces, the geomagnetic Lorentz force, the momentum exchange, would greatly extend the lifetime of the formation and effectively avoid the plume contamination with new control characteristics. This paper summarizes the research methods and achievements in the dynamics and the control of these fields, and puts forward some issues worthy of further study in related fields and the direction of future development.