High-performance computing (HPC) centers consume substantial power, incurring environmental and operational costs. This review assesses how artificial intelligence (AI), including machine learning (ML) and optimization, improves the efficiency of operational HPC systems. Approximately 1,800 publications from 2019 to 2025 were manually screened using predefined inclusion/exclusion criteria; 74 "AI for HPC" papers were retained and grouped into six application areas: performance estimation, performance optimization, scheduling, surrogate modeling, fault detection, and language-model-based automation. Scheduling is the most active area, spanning research-oriented reinforcement-learning schedulers to production-friendly hybrids that combine ML with heuristics. Supervised performance estimation is foundational for both scheduling and optimization. Graph neural networks and time-series models strengthen anomaly detection by capturing spatio-temporal dependencies in production telemetry. Domain-specialized language models for HPC can outperform general-purpose LLMs on targeted coding and automation tasks. Together, these findings highlight integration opportunities such as LLM-based operating-system concepts and underscore the need for advances in MLOps, standardization of AI components, and benchmarking methodology.