The standard financial analysis has proven unable to provide an adequate understanding and therefore a timely warning of the financial crisis. In order to strengthen financial stability, policy makers are looking for new analytical tools to identify and address sources of systemic risk. Complexity theory and network analysis can make a useful contribution. The financial crisis has highlighted the need to look at the links and interconnections in the financial system. Complexity and network theory which can help identify the extent to which the financial system is resilient to contagion as well as the nature of major triggers and channels of contagion. However, the methodological suitability of the premises of complexity theory for financial systems is still debatable. The use of complexity analysis in finance draws on two distinct but related strands of theory: econophysics and econobiology. Each strand is associated with advantages and drawbacks in explaining the dynamics of financial systems. Properly combined, these theories could form a coherent body of theoretical premises that are capable of approximating reality in financial systems, i.e. explain the "stylized facts", better than the traditional financial analysis model, which is crucially based on the false conception of a Gaussian distribution of financial returns.