Knowledge graph (KG) technology is a newly emerged knowledge representation method in the field of artificial intelligence. Knowledge graphs can form logical mappings from cluttered data and establish triadic relationships between entities. Accurate derivation and reasoning of knowledge graphs play an important role in guiding power equipment operation and decision-making. Due to the complex and weak relations from multi-source heterogeneous data, the use of KGs has become popular in research to represent potential information in power knowledge reasoning. In this review, we first summarize the key technologies of knowledge graph representation and learning. Then, based on the complexity and real-time changes of power system operation and maintenance, we present multiple data processing, knowledge representation learning, and the graph construction process. In three typical power operation and fault decision application scenarios, we investigate current algorithms in power KG acquisition, representation embedding, and knowledge completion to illustrate accurate and exhaustive recommendations. Thus, using KGs to provide reference solutions and decision guidance has a significant role in improving the efficiency of power system operations. Finally, we summarize the achievements and difficulties of current research and give an outlook for future, promising roles of KG in power systems.