A network approach to banking is particularly important for assessing financial stability and systemic risk. This approach can be instrumental in capturing the externalities that the risk associated with a single institution may create for the entire system. Indeed, from a financial stability perspective, banks should neither be too-big-to-fail nor too-interconnected-to-fail. A better understanding of network externalities may facilitate the adoption of a macroprudential framework for financial supervision. Network externalities arise when risk-taking behavior of individual institutions affects other institutions and the system as a whole. To guide policy it becomes necessary, in this context, to measure the systemic importance of individual banks, i.e. their capacity to generate contagion in the rest of the system. The analysis of interbank networks can provide this guidance.Against this background we review the literature on interbank networks, which is part of a growing literature on financial networks. The broader financial networks literature is analyzing connections between financial institutions: banks, but also hedge funds, insurance companies, etc. We restrict the survey's focus on the interbank network literature. This survey presents a systematic overview of our current understanding of the structure of interbank networks, of how network characteristics affect contagion in the banking system and of how banks form connections when faced with the possibility of contagion and systemic risk. In particular, we highlight how the theoretical literature on interbank networks offers a coherent way of studying interconnections, contagion processes and systemic risk, while emphasizing at the same time the many challenges that must be addressed before general results on the link between the structure of the interbank network and financial stability can be established.The theoretical literature has generated a number of insights on the effect of the network structure on contagion. A first result is that the number and magnitude of defaults depend on the network topology. There is now substantial research characterizing those structures that tend to propagate default or alternatively that tend to dampen it. An avenue for further research is to have more realistic network structures on which to analyze contagion. Since empirical studies now provide an increasing number of stylized facts on the interbank network topology, research needs to move beyond deriving results on random networks or on overly simplified structures. Furthermore, the fragility of the system depends on the location in the network of the institution that was initially affected. Intuitively, the failure of core banks is more damaging than the failure of a periphery bank. Finally, another main finding is that there is a trade-off between risk sharing via linkages to other banks and contagion risk due to too many linkages. While the existence of the trade-off is not disputed, there is no consensus on whether a complete network dampens or fuels contag...