With the rapid development of pervasive intelligent devices and ubiquitous network technologies, new network applications are emerging, such as the Internet of Things, smart cities, smart grids, virtual/augmented reality, and unmanned vehicles. Cloud computing, which is characterized by centralized computation and storage, is having difficulty meeting the needs of these developing technologies and applications. In recent years, a variety of network computing paradigms, such as fog computing, mobile edge computing, and dew computing, have been proposed by the industrial and academic communities. Although they employ different terminologies, their basic concept is to extend cloud computing and move the computing infrastructure from remote data centers to edge routers, base stations, and local servers located closer to users, thereby overcoming the bottlenecks experienced by cloud computing and providing better performance and user experience. In this paper, we systematically summarize and analyze the post-cloud computing paradigms that have been proposed in recent years. First, we summarize the main bottlenecks of technology and application that cloud computing encounters. Next, we analyze and summarize several post-cloud computing paradigms, including fog computing, mobile edge computing, and dew computing. Then, we discuss the development opportunities of post-cloud computing via several examples. Finally, we note the future development prospects of post-cloud computing.