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While most OECD countries have been rather successful in reducing risks to human lives, health, and the quality of the environment, the record for new global risks such as climate change, pandemics, financial breakdowns, and social inequality is much less convincing. This is the challenge of systemic risks. Since the global financial crisis, it has received rapidly growing attention. However, considerable conceptual confusion mars research on and practical responses to this challenge. We undertake an effort of conceptual clarification, starting with the paradigmatic example of the financial crisis. This leads to a view of global systems as involving an interplay between micro- and macrodynamics internal to the system, with the system simultaneously interacting with its environment. Such dynamics typically show periods of stability, punctuated by situations opening up several possible futures. Alternative global futures, like other prospects, constitute risks for an agent if she considers some of these futures as less desirable than others. Agents may have lexicographic preferences over futures they would like to avoid, so as to consider some futures as just undesirable, but others as catastrophic. If an agent expects some of the relevant futures at a bifurcation point of a global system to be catastrophic in this sense, they are faced with a systemic risk.