Recent advancements in network-connected devices have led to a rapid increase in the deployment of smart devices and enhanced grid connectivity, resulting in a surge in data generation and expanded deployment to the edge of systems. Classic cloud computing infrastructures are increasingly challenged by the demands for large bandwidth, low latency, fast response speed, and strong security. Therefore, edge computing has emerged as a critical technology to address these challenges, gaining widespread adoption across various sectors. This paper introduces the advent and capabilities of edge computing, reviews its state-of-the-art architectural advancements, and explores its communication techniques. A comprehensive analysis of edge computing technologies is also presented. Furthermore, this paper highlights the transformative role of edge computing in various areas, particularly emphasizing its role in power systems. It summarizes edge computing applications in power systems that are oriented from the architectures, such as power system monitoring, smart meter management, data collection and analysis, resource management, etc. Additionally, the paper discusses the future opportunities of edge computing in enhancing power system applications.