Artificial intelligence (AI) workloads are creating large, power-electronic loads whose effects on power systems depend on location, temporal variability, controllability, and interactions with other loads and resources. Annual electricity consumption alone cannot capture these effects. This review examines how AI data centers affect power systems stability, renewable-energy integration, and low-carbon planning by tracing the power-delivery chain from accelerators and workloads through rack converters, uninterruptible power supplies (UPS), storage, and microgrids to the transmission point of interconnection. Reported oscillatory events and multi-gigawatt load transfers highlight how facility responses can amplify disturbances, while programmable workloads and controllable power converters offer opportunities for demand flexibility. Challenges and mitigation strategies are organized across device, rack, facility, and power systems levels, spanning millisecond-to-year timescales. A bandwidth-matching framework relates disturbances to the response capabilities of mitigation resources. The review distinguishes computational energy efficiency from power systems and sustainability outcomes: lower energy consumption per token does not necessarily reduce peak demand, electrical disturbances, or carbon emissions. It examines how coordinated workload scheduling, grid-interactive UPS systems, storage, high-voltage DC distribution, and flexible interconnection can support reliability, efficiency, and decarbonization. Key research needs include dynamic load models, high-bandwidth telemetry, carbon-and grid-aware scheduling, and mechanisms for valuing flexible computational demand.