Abstract: Matching control (also known as inertia synchronization control, DC voltage synchronization control, etc.) is one of grid-forming control methods that can be applied to photovoltaic power generation, wind power generation, static reactive power compensation and HVDC power transmission where the DC side is not an ideal DC source. The existing researches focus more on the imitation between the matching control and the rotor inertia of synchronous generators, and usually lack the in-depth analysis of the synchronous damping and small-disturbance synchronous stability mechanism. Therefore, this paper firstly reviews the research and development history of matching control, and then proposes the classification of synchronous damping based on feedback and feedforward controls. Meanwhile, from the aspects of DC-side additional resistance, the grid-side additional damping control, and the machine-side additional damping control, this paper compares and summarizes the various matching control methods as well as their small-disturbance synchronous stability mechanism. Finally, four typical application scenarios of matching control, including photovoltaic power generation, wind power generation, static var generation, and HVDC power transmission, are analyzed in this paper, which is also helpful to enhance the value cognition and characteristic ability cognition of matching control method in practical applications.