Edge computing is one of the key driving forces to enable Beyond 5G (B5G) and 6G networks. Due to the unprecedented increase in traffic volumes and computation demands of future networks, Multi-access Edge Computing (MEC) is considered as a promising solution to provide cloud-computing capabilities within the radio access network (RAN) closer to the end users. There has been a huge amount of research on MEC and its potential applications; however, very little has been said about the key factors of MEC deployment to meet the diverse demands of future applications. In this article, we present key considerations for edge deployments in B5G/6G networks including edge architecture, server location and capacity, user density, security etc. We further provide state-of-the-art edge-centric services in future B5G/6G networks. Lastly, we present some interesting insights and open research problems in edge computing for 6G networks.