The term ’systemic risk’ commonly denotes the risk that a whole system consisting of many interacting agents fails. It is a macroscopic property which emerges from the nonlinear interactions of agents. In fact, ’systemic risk’ already implies that the failure of the system cannot be fully explained by the failure of a single agent. Instead, one has to understand how such singular failures are able to spread through the whole system, affecting other agents. Here, in addition to network topology, dynamic mechanisms such as contagion (similar to epidemic processes or herding behavior), reinforcement (of prevailing trends), and redistribution (e.g. of load, stress, or debt) play a considerable role. The talk aims at categorizing some of the existing models in a common framework, first, and discussing a specific model of financial networks, afterwards, to elucidate the critical conditions for the breakdown of a system.