The foundational enhancements, i.e. high bandwidth, low latency and large connection, for future 5G and cellular-V2X (C-V2X) network will foster the connected and automatic vehicle (CAV) to be greatly promoted in large scale. In the meanwhile, a multitude of practices in traffic big data mustering, cooperative vehicle and infrastructure system and intelligent vehicle utilization would bring a pressing requirement on high qualified computation platform. The centralized cloud-based computing platform can no longer meet these needs, in reverse, by arranging the computing platform in close proximity to roadside infrastructures and connected vehicles, the data routing process will become faster and computing workloads can be significantly mitigated, therefore balancing the time-critical applications in front-end or in centralized back-end platform. This paper reviews the current progress and development on connected vehicle deployment and applications, in particular the subfields of MEC-enabled V2X systems for resolving the time-critical traffic safety problems. Then, an overview of multi-access edge computing (MEC) and C-V2X system deployment is presented, along with a detailed category in aspects of advanced driving assistant systems (ADAS), cooperative vehicle and infrastructure system and vulnerable road user (VRU) based on this framework. We further illustrate that the deployment of MEC (Multi-Access Edge Computing) can effectively be integrated with V2X network and expand cloud computing capabilities and network performance at the edge. By deploying applications and services at the local MEC, it substantially trims the links of data transmission, and reduces the bandwidth occupation as well as the end-to-end delay, thus is able to meet the basic requirements of connected and automatic vehicle applications.