Future 5G technologies are expected to overcome the challenges of next generation networks aiming to tackle the novel and manifold business requirements associated to different vertical sectors. Extraordinarily high speeds and capacity, multi-tenancy, heterogeneous technologies convergence, on-demand service-oriented resource allocation or even coordinated, automated management of resources are only few examples of the complex demands 5G aims to undertake. The shift from centralised cloud computing-based services towards data processing at the edge is becoming one of the fundamental components envisaged to enable those future 5G technologies. Edge computing is focused on pushing processing to the network edge where all the actual interactions in the access networks take place and the critical low-latency processing occurs. Combination of Network Functions Virtualisation (NFV) and edge computing technologies and mechanisms provides a wide range of novel opportunities for added-value service provisioning covering different features required in future access networks, such as Quality of Service (QoS), security, multi-tenancy, and low-latency. This chapter provides an overview of edge computing technologies, from supporting heterogeneous infrastructure up to service provisioning methodologies related to the application-specific requirements. It describes the role of edge computing and NFV in future 5G mobile networks. It also provides an insight into how edge computing can potentially facilitate and expedite provisioning of security in 5G networks. The manuscript analyses the role of the networking resources in edge computing-based provisioning, where the demands of 5G mobile networks are to be met with wireless networking technologies, which in essence are different to wired technologies present in core data centres. Initial results obtained from the evaluations of wireless fog networking backhauls are presented and the challenges ahead of the actual implementation of those technologies are also analysed in the chapter.