Variational mode decomposition (VMD), a very active branch in the field of adaptive signal decomposition, has become a hot research direction in the field of signal processing. VMD shows good performance in processing non-stationary and nonlinear signals. Aiming at VMD model and its parameter selection, many extended models and parameter optimization methods have been studied. This article reviews the research progress of VMD in recent decade, summarizes and analyzes the relevant literature. Firstly, it analyzes the principle advantages of VMD and its application potential in various fields. Secondly, according to the matching ability of the model to different signal types, the different characteristics and applicable scenarios of extended models of VMD are summarized by classification. Then, the research progress of parameter optimization methods for VMD and its extended models are summarized to discuss and analyze the characteristics of different model parameter optimization methods and the latest research trends. Finally, 6 prospects are put forward for the future development of VMD, pointing out the direction for subsequent research.