Abstract: The characteristics of high proportion renewable energy and power electronics in new power systems bring great challenges to power system analysis and decision. With deep learning (DL) as a typical technique, data-driven techniques, which are specialized in large-scale high-dimensional nonlinear data modeling, become increasingly attractive in the field of power system analysis and decision. As a famous DL family, graph deep learning (GDL) extends DL for irregular topological data and promotes its practical application in power systems. This paper briefly summarizes the task-specific demands of power system analysis and decision and its DL-driven applications at first. Based on advances and frontal techniques of GDL, this paper provides a comprehensive review on the advantages and disadvantages of GDL. Finally, the future development of GDL is discussed concerning its generality/transferability, reliability as well as interpretability.