Alexander Teytelboym University of Oxford A cascade is an irreversible (at least in some time frame) process that propagates through a network. Network cascades are common phenomena in many physical, social and economic networks; just think of bank failures or diffusion of social products. We review several theoretical models of cascades and discuss their empirical applications. Finally, we introduce the concept of cascade centrality, which measures how influential a node is for a cascade in a network. This new concept allows us to tackle questions of network design and apply it to studying competitive diffusion of products in a social network.