The growing reliability, safety and environmental risks associated with aging energy infrastructure- such as power transmission systems, oil and gas piping, nuclear plants and offshore systems- are increased as systems continue to be used beyond their designed design life in a state of increased uncertainty. Conventional maintenance approaches, which rely mostly on isochronic schedules or states of condition have not been effective in dealing with low likelihood, high-consequence failures of such assets. Risk-Based Maintenance (RBM) has thus become an imperative decision structure, which blatantly incorporates the probability of failure, severity of consequences, and asset criticalness. Meanwhile, machine learning (ML) has become a popular data-driven degradation modelling, fault detection and predictive maintenance tool. Nevertheless, the speed of ML application proliferation has exceeded the pace of their inclusion in the systematic risk-centric maintenance theory. This is an analytical summary of ML methods of RBM in aging energy infrastructure and focuses on conceptual integration, as opposed to algorithmic benchmarking. It looks at the role played by supervised learning, deep learning, probabilistic ML, and reinforcement learning in the various aspects of RBM, and the various challenges posed by the data imbalance, non-stationary degradation, weak interpretability, and weak connection to physical failure. This analysis shows that high predictive accuracy does not always result in effective maintenance decisions out of the context of explicit risk integration, consequence modelling and human supervision. This review makes it clear that ML is a decision-support enabler rather than a substitute to probabilistic risk assessment by merging knowledge in the energy domain and methodological paradigm. The study also ends by outlining major research priorities, such as physics-informed and hybrid probabilistic ML, digital twins, explainable AI and cyber-resilient maintenance analytics.