The latest financial crisis has painfully revealed the dangers arising from a globally interconnected financial system. Conventional approaches based on the notion of the existence of equilibrium and those which rely on statistical forecasting have seen to be inadequate to describe financial systems in any reasonable way. A more natural approach is to treat financial systems as complex networks of claims and obligations between various financial institutions present in an economy. The generic framework of complex networks has been successfully applied across several disciplines, e.g., explaining cascading failures in power transmission systems and epidemic spreading. Here we review various network models addressing financial contagion via direct inter-bank contracts and indirectly via overlapping portfolios of financial institutions. In particular, we discuss the implications of the "robust-yet-fragile" nature of financial networks for cost-effective regulation of systemic risk.
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