The edge computing (EC) paradigm brings computation and storage to the edge of the network where data is both consumed and produced. This variation is necessary to cope with the increasing amount of network-connected devices and data transmitted, that the launch of the new 5G networks will expand. The aim is to avoid the high latency and traffic bottlenecks associated with the use of Cloud Computing in networks where several devices both access and generate high volumes of data. EC also improves network support for mobility, security, and privacy. This paper provides a discussion around EC and summarized the definition and fundamental properties of the EC architectures proposed in the literature (Multi-access Edge Computing, Fog Computing, Cloudlet Computing, and Mobile Cloud Computing). Subsequently, this paper examines significant use cases for each EC architecture and debates some promising future research directions.