Abstract: With the increasing uncertainty of the generation, transmission, and consumption sides in new power systems, the complexity and scale of power system topology relationship are continuously growing. Conventional data analysis methods for Euclidean space often exhibit poor performance and low accuracy when representing the topological structures relationship with multi-source heterogeneous and irregular characteristics. Graph Neural Networks (GNNs) are capable of capturing complex dependency relationship between different nodes and edges, and effectively mining spatiotemporal features in non-Euclidean data structures, are therefore suitable for the perception and modeling of complex power system topologies. In this context, this paper builds upon previous research progress, providing the definition and characteristics of GNNs, and discussing the unique features and advantages of different variants GNNs. After that, it summarizes the current applications of GNNs in power system state perception, prediction, and graph-based power flow calculation, aiming to explore the suitability of GNNs for new power systems from the perception-prediction-optimization perspectives. Finally, a summary and outlook on the potential challenges and future development directions for GNNs are provided.