The concept of Virtual Synchronous Machines (VSM) has been introduced in the last decade with the aim of providing the controllability and stability features of a classical synchronous machine to a power electronics converter. This paper has reviewed the background for the various implementations and control structures proposed for the VSM concept in the literature, and classified the presented proposals according to the VSM detailing level and the control structure used for implementation. Finally, the trends of virtual synchronous generator technology were discussed.