Resilience, the ability to resist or recover from disturbance, is ubiquitous in ecology but defined and measured in different ways. The evaluation of resilience depends on decisions made by the investigator(s), including the variables measured. Here we highlight an under-appreciated observation: there is no canonical definition of overall resilience and such a definition may be unattainable. Therefore, we make four key points. First, we highlight and categorize the diverse variables used to measure ecological resilience and place them in a conceptual model. Second, we argue that different relevant variables often respond very differently to disturbance and prove that no system can be completely resilient to a press disturbance (‘Necessary Non-resilience’). Third, we demonstrate with four examples how categorization of diverse resilience variables and a conceptual model can stimulate new research questions. Fourth, we apply our framework to four empirical case studies to demonstrate the biological relevance of such new directions. Overall, we argue that advancing resilience ecology will require a deeper consideration of variable choice, how different resilience variables interact, the inevitable failure of resilience in some variables, and how these ideas can foster new, general research directions.