With the emergence of self-driving technology and the ever-increasing demand of bandwidth-hungry applications, providing the required latency, security and computational capabilities is becoming a challenging task. Although being evolving, traditional vehicular radio access technologies, namely WLAN/IEEE 802.11p and cellular networks cannot meet all the requirements of future Cooperative, Connected and Automated Mobility (CCAM). In addition, current vehicular architectures are not sufficiently flexible to support the highly heterogeneous landscape of emerging communication technologies, such as mmWave, Cellular Vehicle-to-Everything (C-V2X), and Visible Light Communication (VLC). To this aim, Multi-access Edge Computing (MEC) has been recently proposed to enhance the quality of passengers experience in delay-sensitive applications. In this paper, we discuss the in-premises features of MEC and the need of supporting technologies, such as Software Defined Networking (SDN) and Network Function Virtualization (NFV), to fulfil the requirements in terms of responsiveness, reliability and resiliency. The latter is of paramount importance for automated services, which are supposed to be always-on and always-available. We outline possible solutions for mobility-aware computation offloading, dynamic spectrum sharing, and interference mitigation. Also, by revealing MEC-inherent security vulnerabilities, we argue for the need of adequate security and privacy-preserving schemes in MEC-enabled vehicular architectures.