This thesis thoroughly explores Multi-Access Edge Computing (MEC) and Vehicular Networking in the evolving 5G and 6G environments. The study combines three main areas of research: surveying MEC with focuses on vehicular networks, improving energy-efficient service mobility management using Software-Defined Networking (SDN) in these networks, and proposing energy-efficient offloading policies for large-scaleMECsystems with task handover. This thesis not only addresses pivotal challenges in the field but also sets new benchmarks in network resource management for the data-intensive and dynamic conditions characteristic of modern communication networks. The first core area of this thesis presents an extensive survey on the role of MEC in vehicular networks. This part of the research highlights the critical role of MEC in supporting task offloading, resource allocation, and managing inter-server communications, all essential for low-latency, real-time applications in vehicular contexts. The survey comprehensively covers the architectural framework of MEC, its applications, and the emerging challenges in integrating MEC within vehicular networks. This section is instrumental in delineating the current landscape and future potential of MEC applications in these networks, thus bridging the gap between traditional cloud computing capabilities and the emerging demands of edge computing, and also the challenge of creating energy-efficient offloading strategies within large-scale MEC systems. This focus is pivotal given the increasing complexity brought about by the heterogeneity of mobile users and network components and their inherent mobility. The exploration extends to MEC-enabled vehicular networks, revealing the synergy between MEC and these networks. This phase also acknowledges the challenges of vehicular mobility, privacy, and security, which are paramount in this context. The second phase focuses on the proposed SDN-MEC-EE approach, a novel SDN-assisted energy-efficient MEC framework. This approach is characterized by its energy efficiency, achieving up to a 15% reduction in power consumption for compute-intensive services and an average of 20% reduction for latency-sensitive services compared to conventional SDN-MEC models. Through comprehensive simulations, the SDN-MEC-EE framework demonstrates exceptional throughput and consistently lower latency levels, validating its suitability for high-speed, real-time demands in future vehicular networks. An essential element of this approach is the strategic use of Docker containers over VMs, which significantly reduces service migration delays, enhancing network stability and user experience. The SDN-MEC-EE approach’s superiority is further confirmed in its comparative performance against Distributed Mobility Management (DMM) technologies, showcasing its ability to maintain lower latency and more stable control overheads. In this thesis, we also tackle the intricate challenge of achieving energyefficient task offloading in MEC systems with handover, particularly targeting at realistically large networks. By adopting restless-bandit-based (RBB) resource allocation techniques, we aim to meticulously minimize the long-run average power consumption, taking into account the dynamic fluctuations of channel states and network resources. We propose a novel RBB-based resource allocation scheme, referred to as HEE-ACC, with theoretically bounded performance degradation - it approaches optimality as the network system becomes sufficiently large. Within this scheme, we further delineate two nearoptimal scheduling policies, HEE-ACC-zero and HEE-ALRN, which prioritise the selection of computing and communication resources based on their marginal costs. Through analytical discussions and extensive simulations using both emulated and real-world system parameters, we demonstrate the scalability and effectiveness of our proposed policies. This comprehensive study not only advances the theoretical framework for energy-efficient computing in MEC systems but also offers practical insights for managing resource allocation in the face of task handovers, thereby contributing significantly to the field of mobile computing. This thesis focuses on improving the performance and efficiency of mobile networks, specifically in the areas of MEC in the 5G and vehicular network domains. The research outcomes not only provide an essential understanding of MEC and its applications but also propose innovative approaches like the SDN-MEC-EE approach and HEE-ACC scheme. These approaches facilitate improved network performance, energy efficiency, and user experience in the fast-changing field of mobile communications. The proposed SDN-MEC-EE approach, with its focus on energy conservation, throughput optimization, and latency reduction, sets a new promising method for future mobile networks. The HEE-ACC policies offer a scalable, near-optimal approach for tackling large-scale MEC systems in high-mobility environments. The comprehensive exploration conducted in this thesis underscores the critical role of MEC in the current networking landscape and the future potential of HEE-ACC scheduling policies and SDN-MEC-EE approach in shaping the next generation of latency-sensitive applications and services.