As mobile internet and Internet of Things (IoT) applications continue to grow, traditional centralized cloud computing faces significant challenges such as high latency, low spectral efficiency, and non-adaptive machine communication. To address these challenges, a new trend has emerged that shifts the function of cloud computing to edge devices in the network. This paper provides a comprehensive tutorial on three typical edge computing technologies: mobile edge computing, cloudlets, and fog computing. It summarizes and compares the standardization efforts, principles, architectures, and applications of these technologies. The differences between mobile edge computing and fog computing from a radio access network perspective are highlighted, and the characteristics of a fog computing-based radio access network are discussed. The paper concludes by identifying open issues and future research directions in this field.