The recent outbreak of Ebola Virus Disease (EVD) in West Africa has drawn attention to the role and responsiveness of health systems in the face of shock. It brought into sharp focus the idea that health systems need not only to be stronger but also more ‘resilient’. In this article, we argue that responding to shocks is an important aspect of resilience, examining the health system behaviour in the face of four types of contemporary shocks: the financial crisis in Europe from 2008 onwards; climate change disasters; the EVD outbreak in West Africa 2013–16; and the recent refugee and migration crisis in Europe. Based on this analysis, we identify ‘3 plus 2’ critical dimensions of particular relevance to health systems’ ability to adapt and respond to shocks; actions in all of these will determine the extent to which a response is successful. These are three core dimensions corresponding to three health systems functions: ‘health information systems’ (having the information and the knowledge to make a decision on what needs to be done); ‘funding/financing mechanisms’ (investing or mobilising resources to fund a response); and ‘health workforce’ (who should plan and implement it and how). These intersect with two cross-cutting aspects: ‘governance’, as a fundamental function affecting all other system dimensions; and predominant ‘values’ shaping the response, and how it is experienced at individual and community levels. Moreover, across the crises examined here, integration within the health system contributed to resilience, as does connecting with local communities, evidenced by successful community responses to Ebola and social movements responding to the financial crisis. In all crises, inequalities grew, yet our evidence also highlights that the impact of shocks is amenable to government action. All these factors are shaped by context. We argue that the ‘3 plus 2’ dimensions can inform pragmatic policies seeking to increase health systems resilience.