With the introduction of 5G and the Internet of Things, Multi-access Edge Computing (MEC) has become an evolving distributed compute and storage capability at the network edge. MEC will support task offloading, mobility, resource allocation, and management of inter-server communications to improve quality of service and satisfy real-time applications that require low latency. Thus, MEC is regarded as a crucial capability that will provide computation and storage at the network edge as an extension of the more traditional cloud. By placing MEC at the network edge, a broad range of new applications and services can be offered in close proximity to users, including support for vehicular networks. This paper provides a current and comprehensive review of MEC-enabled vehicular networks. It first introduces MEC by providing a definition, architecture, applications, and challenges. The paper then investigates MEC support for vehicular network applications and services and identifies current research and future challenges.