In this paper we review recent advances in financial economics in relation to the measurement of systemic risk. We start by reviewing studies that apply traditional measures of risk to financial institutions. However, the main focus of the review is on studies that use network analysis paying special attention to those that apply complex analysis techniques. Applications of these techniques for the analysis and pricing of systemic risk has already provided significant benefits at least at the conceptual level but it also looks very promising from a practical point of view.