Modern financial systems exhibit a high degree of interdependence. There are different possible sources of connections between financial institutions, stemming from both the asset and the liability side of their balance sheet. For instance, banks are directly connected through mutual exposures acquired on the interbank market. Likewise, holding similar portfolios or sharing the same mass of depositors creates indirect linkages between financial institutions. Broadly understood as a collection of nodes and links between nodes, networks can be a useful representation of financial systems. By providing means to model the specifics of economic interactions, network analysis can better explain certain economic phenomena. In this paper we argue that the use of network theories can enrich our understanding of financial systems. We review the recent developments in financial networks, highlighting the synergies created from applying network theory to answer financial questions. Further, we propose several directions of research. First, we consider the issue of systemic risk. In this context, two questions arise: how resilient financial networks are to contagion, and how financial institutions form connections when exposed to the risk of contagion. The second issue we consider is how network theory can be used to explain freezes in the interbank market of the type we have observed in August 2007 and subsequently. The third issue is how social networks can improve investment decisions and corporate governance. Recent empirical work has provided some interesting results in this regard. The fourth issue concerns the role of networks in distributing primary issues of securities as, for example, in initial public offerings, or seasoned debt and equity issues. Finally, we consider the role of networks as a form of mutual monitoring as in microfinance.