The Internet of Things (IoT) allows communication between devices, things, and any digital assets that send and receive data over a network without requiring interaction with a human. The main characteristic of IoT is the enormous quantity of data created by end-user’s devices that needs to be processed in a short time in the cloud. The current cloud-computing concept is not efficient to analyze very large data in a very short time and satisfy the users’ requirements. Analyzing the enormous quantity of data by the cloud will take a lot of time, which affects the quality of service (QoS) and negatively influences the IoT applications and the overall network performance. To overcome such challenges, a new architecture called edge computing — that allows to decentralize the process of data from the cloud to the network edge has been proposed to solve the problems occurred by using the cloud computing approach. Furthermore, edge computing supports IoT applications that require a short response time and consequently enhances the consumption of energy, resource utilization, etc. Motivated by the extensive research efforts in the edge computing and IoT applications, in this paper, we present a comprehensive review of edge and fog computing research in the IoT. We investigate the role of cloud, fog, and edge computing in the IoT environment. Subsequently, we cover in detail, different IoT use cases with edge and fog computing, the task scheduling in edge computing, the merger of software-defined networks (SDN) and network function virtualization (NFV) with edge computing, security and privacy efforts. Furthermore, the Blockchain in edge computing. Finally, we identify open research challenges and highlight future research directions.