Economic stability is dependent on the effective functioning and resilience of energy systems. Resilience is a term used across all research disciplines and in everyday discourse. As a concept it purports to serve as a useful indicator of sustainability and robustness, but it has proved difficult to measure. Ecological resilience, psychological resilience, risk management and energy security are all fields of research in which measures of the ability to respond to the unexpected are sought. The goal is to build adaptive capacity but quite different methods have been developed to achieve this end. Research on energy security, in particular, has focused on the security of oil supplies, not resilience or the adaptive capacity of the energy system or the role that renewable energy plays in building such capacity. This paper discusses how different disciplines seek to measure and build resilience and explores its connection with the state or quality of a system’s adaptive capacity. When the parameters of redundancy and diversity are present, resilience is enhanced. For this reason, in energy systems we must understand the size and scope of the key parameters required to facilitate the development of adaptive capacity and to build resilience that can enhance economic stability.