This article reviews recent works applying machine learning (ML) techniques in the context of energy systems' reliability assessment and control. We showcase both the progress achieved to date as well as the important future directions for further research, while providing an adequate background in the fields of reliability management and of ML. The objective is to foster the synergy between these two fields and speed up the practical adoption of ML techniques for energy systems reliability management. We focus on bulk electric power systems and use them as an example, but we argue that the methods, tools, etc. can be extended to other similar systems, such as distribution systems, microgrids, and multienergy systems.