The virtual synchronous machine (VSM) method is a power electronics based approach which was first introduced by Beck and Hesse in 2007 for renewable energy integration modeling. This method controls grid-connected renewable energy sources as electromechanical synchronous machines, which makes renewable energy sources behave as conventional power generation stations if viewed from the power grid. During the last decade, some developments have been made to operate power electronic converters as VSMs, which offers a promising way to design advanced control systems for renewable energy integration. Most publications on this topic actually occurred within the past two years. As an emerging new method with huge potential, the VSM method has been used to reduce voltage and frequency fluctuation of renewable energy sources, and improve power system stability. In this paper, a comprehensive literature review is conducted for the VSM method. The principle, and current state of the art control techniques to implement this method are reviewed and summarized in the paper.