The recent developments in the research area are significantly advancing the integration of renewable energy, decentralized network topologies, and AI-driven resource management in edge computing environments. There is a notable shift towards sustainable solutions, with a focus on leveraging renewable energy sources to power 5G Fixed Wireless Access (FWA) in rural areas, thereby reducing operational costs and environmental impact. This trend is complemented by the exploration of decentralized network topology designs, which aim to optimize task offloading in Mobile Edge Computing (MEC) by enhancing computational efficiency through innovative three-layered structures. Additionally, the field is witnessing a surge in the application of AI, particularly in the realm of generative AI, to manage and allocate resources in wireless edge networks, ensuring high-quality, low-latency services despite resource constraints. These advancements collectively underscore a move towards more adaptive, efficient, and sustainable edge computing solutions, driven by innovative approaches in energy modeling, network topology optimization, and AI-based resource allocation.