Grid vulnerability is one of the core content of large-scale power grid security research. In the context of frequent blackouts in domestic and foreign power grids, traditional methods are difficult to effectively analyze the generation and propagation process of large-scale cascading failures from a macroscopic perspective. With the continuous development and universal application of complex network theory research, this method breaks through the limitations of traditional methods in analyzing cascading failures, and provides a new perspective and direction for studying the vulnerability of large power grids. This article first introduces the two basics of complex networks and their common evaluation indicators, followed by detailed descriptions of node importance discovery, identification of vulnerable lines in the power grid, cascading failures in a single network, and cascading failures between dependent networks, and other aspects of the research development and application, and comprehensive analysis of the power grid operation status. Finally, from the perspective of complex network theory, the future research direction of grid vulnerability is summarized and prospected.