Most human interactions today take place with the mediation of information and communications technology. This is extending the boundaries of interdependence: the group of reference, ideas and behaviour to which people are exposed is larger and less restricted to old geographical and cultural boundaries; but it is also providing more and better data with which to build more informative models on the effects of social interactions, amongst them, the way in which contagion and cascades diffuse in social networks. Online data are not only helping us gain deeper insights into the structural complexity of social systems, they are also illuminating the consequences of that complexity, especially around collective and temporal dynamics. This paper offers an overview of the models and applications that have been developed in what is still a nascent area of research, as well as an outline of immediate lines of work that promise to open new vistas in our understanding of cascading behaviour in social networks.