Artificial intelligence has shifted from a software-centric discipline to an infrastructure-driven system. Training and inference at scale now depend on tightly connected data centers, high-capacity optical networks, and energy systems operating close to their physical and environmental limits. In this context, control over data and algorithms is not enough. Real AI sovereignty depends on the ability to deploy, operate, and adapt infrastructure under constraints such as energy availability, sustainability requirements, and network reach. This tutorial-survey introduces the concept of AI infrastructure sovereignty, defined as the ability of a region, operator, or nation to maintain operational control over AI systems within these constraints. The central idea is that sovereignty emerges from the joint design of three layers: AI-oriented data centers, optical transport networks, and control frameworks that provide real-time visibility and coordination across them. We first examine how AI workloads are reshaping data center design, pushing power densities higher, increasing cooling demands, and tightening the relationship with local energy systems. In this setting, factors such as carbon intensity and water usage become hard limits on where and how AI can be deployed. We then look at optical networks as the backbone of distributed AI, showing how latency, capacity, failure domains, and jurisdictional boundaries directly influence what can be achieved in practice. Building on this foundation, the paper highlights the role of telemetry, agentic AI, and digital twins as key enablers of operational sovereignty. Together, they make it possible to monitor, coordinate, and validate system behavior across compute, network, and energy domains in a closed loop.

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