Future 5G wireless networks are confronted with various challenges such as exponentially increasing mobile traffic and new services requiring high backhaul bandwidth and low latency. Integrating mobile edge computing (MEC) into 5G network architectures may be a promising solution. First of all, this paper introduces the functional framework of MEC systems. Then the standardization progress of MEC in 5G is presented. Supporting MEC, the functionalities of 5G core network are described in detail. Given MEC deployment strategies and the mobile network architectures of future 5G, a MEC coordinated 5G network architecture is proposed, which demonstrates that 5G will be a network featured by the coordination of communications and multi-level computing. The proposed network architecture can support various communication modes adaptively and enable the resource sharing efficiently with virtualization technologies. Some researches have been carried out on MEC coordinated 5G, such as basic theorems related to the 5G network capacity concerning both the communication and computing resources, and key technologies including the joint optimization of communication and computing resources, multicast based on computing and cache, and bandwidth-saving transmission. It can be seen that much more efforts need to be put on MEC coordinated 5G before the network can be fully understood.