Sending data to the cloud for analysis was a prominent trend during the past decades, driving cloud computing as a dominant computing paradigm. However, the dramatically increasing number of devices and data traffic in the Internet-of-Things (IoT) era are posing significant burdens on the capacity-limited Internet and uncontrollable service delay. It becomes difficult to meet the delay-sensitive and context-aware service requirements of IoT applications by using cloud computing alone. Facing these challenges, computing paradigms are shifting from the centralized cloud computing to distributed edge computing. Several new computing paradigms, including Transparent Computing, Mobile Edge Computing, Fog Computing, and Cloudlet, have emerged to leverage the distributed resources at network edge to provide timely and context-aware services. By integrating end devices, edge servers, and cloud, they form a hierarchical IoT architecture, i.e., End-Edge-Cloud orchestrated architecture to improve the performance of IoT systems. This article presents a comprehensive survey of these emerging computing paradigms from the perspective of end-edge-cloud orchestration. Specifically, we first introduce and compare the architectures and characteristics of different computing paradigms. Then, a comprehensive survey is presented to discuss state-of-the-art research in terms of computation offloading, caching, security, and privacy. Finally, some potential research directions are envisioned for fostering continuous research efforts.