This chapter explores the application of AI-driven approaches for optimizing resource allocation in video streaming systems, focusing on the dynamic management of cloud and edge resources. Techniques such as reinforcement learning, deep Q-networks, and predictive analytics are discussed as key enablers for minimizing costs, reducing latency, and improving the Quality of Experience (QoE) for users. AI algorithms allow streaming platforms to balance workloads across cloud and edge environments, adaptively allocating computing power, bandwidth, and storage based on real-time network conditions. Case studies demonstrate significant performance gains achieved through AI-based resource management, including cost reductions and improved streaming quality. The chapter also addresses challenges related to scalability, model accuracy, and data availability in AI implementations. Future trends such as federated learning and the integration of supporting technologies like 5G and blockchain are highlighted as potential avenues for enhancing resource optimization in the evolving landscape of video streaming. The presented insights offer a comprehensive understanding of how AI techniques can transform cloud and edge resource management, paving the way for more efficient, scalable, and cost-effective video delivery systems.