This paper develops a broad concept of systemic risk, the basic economic concept for the understanding of financial crises. It is claimed that any such concept must integrate systemic events in banking and financial markets as well as in the related payment and settlement systems. At the heart of systemic risk are contagion effects, various forms of external effects. The concept also includes simultaneous financial instabilities following aggregate shocks. The quantitative literature on systemic risk, which was evolving swiftly in the last couple of years, is surveyed in the light of this concept. Various rigorous models of bank and payment system contagion have now been developed, although a general theoretical paradigm is still missing. Direct econometric tests of bank contagion effects seem to be mainly limited to the United States. Empirical studies of systemic risk in foreign exchange and security settlement systems appear to be non-existent. Moreover, the literature surveyed reflects the general difficulty to develop empirical tests that can make a clear distinction between contagion in the proper sense and joint crises caused by common shocks, rational revisions of depositor or investor expectations when information is asymmetric ("information-based" contagion) and "pure" contagion as well as between "efficient" and "inefficient" systemic events. currency crises