The thesis contains three chapters on financial contagion and instability. Chapter 1 is devoted to a discussion of financial networks and systemic risk. I provide an overview of the literature that emphasises various channels of shock propagation through network connections, such as networks of contractual obligations or overlapping asset holdings. Two topics are discussed: interconnectedness and liquidity. Chapter 2 is concerned with post-trade netting in derivatives markets. We focus on two types of post-trade risk reduction (PTRR) services that apply multilateral netting techniques: portfolio re-balancing and portfolio compression. We first provide a mathematical characterisation of their netting mechanisms and then analyse the effects from a network perspective by considering contagion arising from defaults on variation margin payments. We provide sufficient conditions for systemic risk reduction and illustrate that post-trade netting can be harmful. We also explore the consequences when institutions strategically react to liquidity stress by delaying their payments. Chapter 3 deals with financial vulnerability. I introduce an index that formulates financial vulnerability from a systemic perspective. It is derived from a model that captures spillover losses in the system caused by deleveraging and joint liquidation of illiquid assets. Using data on U.S. banks around the Great Depression and the Global Financial Crisis, I show that the index is easy to implement and can be used for monitoring financial instability, setting the countercyclical capital buffer, and analysing historical banking crises.