As more and more power electronic based generation units are integrated into power systems, the stable operation of power systems has been challenged due to the lack of system inertia. In order to solve this issue, the virtual synchronous generator (VSG), in which the power electronic inverter is controlled to mimic the characteristics of traditional synchronous generators, is a promising strategy. In this paper, the representation of the synchronous generator in power systems is firstly presented as the basis for the VSG. Then the modelling methods of VSG are comprehensively reviewed and compared. Applications of the VSG in power systems are summarized as well. Finally, the challenges and future trends of the VSG implementation are discussed.