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Sustainable systems must maintain their function even in the event of disruptions in order to be considered truly sustainable. The theory of resilience concerns the behavior of systems during and aftershocks. Initially, modern understanding of resilience focused on ecological systems; however, the theory was extended to include the ecological aspects and the also social aspects of a system. As a result of climate change, increased efforts have been made to ensure energy systems are more sustainable. The issue of resilience has therefore significantly gained importance of late to energy systems. In the future, modern energy systems will be increasingly exposed to disruptions, whether due to climate change, terrorism, or variable power supply from renewable energy sources. Protecting energy systems from all these threats is only possible at great cost, but it is much more sensible to design resilient systems that can quickly resume their system function after a disturbance. This review looks at research into the resilience and its application to energy systems and identifies similarities and differences. Starting with Holling's contribution to resilience, the development of the theory is examined and the different definitions are compared. The differences between engineering and ecological resilience are also discussed. Additionally, the review examines, on the one hand, criticism of the theory of resilience and, on the other hand, remaining questions in relation to the application of resilience, such as the system's state after the disruption. The paper subsequently examines the application of the theory of resilience to different energy systems. The review concludes with an outlook on the possibility of operationalizing resilience for energy systems.