Propagation of balance-sheet or cash-flow insolvency across financial institutions may be modeled as a cascade process on a network representing their mutual exposures. In the first part, we derive rigorous asymptotic results for the magnitude of contagion in a large financial network and give an analytical expression for the asymptotic fraction of defaults, in terms of network characteristics. Our results extend previous studies on contagion in random graphs to inhomogeneous directed graphs with a given degree sequence and arbitrary distribution of weights. We introduce a criterion for the resilience of a large financial network to the insolvency of a small group of financial institutions and quantify how contagion amplifies small shocks to the network. Our results emphasize the role played by 'contagious links' and show that institutions which contribute most to network instability in case of default have both large connectivity and a large fraction of contagious links. The asymptotic results show good agreement with simulations for networks with realistic sizes. This part of talk is based on joint work with Rama Cont and Andreea Minca. In the second part, we consider the problem of a lender of last resort who seeks to minimize the magnitude of contagion under budget constraints. In case the lender observes the interbank exposures progressively, as banks report their exposures to banks in default, we can model distress propagation under intervention as a Markov Decision Process. We find the optimal intervention policy as a result of Hamilton Jacobi Bellman equations. Our results show that, in the case of non-anticipative information, the optimal strategy depends in a non-linear way on the fraction of banks that use short-term funding. This part is based on a joint work with Jean-Philippe Chancelier, Andreea Minca and Agnes Sulem.