We survey the recent literature on theoretical models of diffusion in social networks and the application of these models to viral marketing. To put this work in context, we begin with a review of the most common models that have been examined in the economics and sociology literature, including local interaction games, threshold models, and cascade models, in addition to a family of models based on Markov random fields. We then discuss a series of recent algorithmic and analytical results that have emerged from the computer science community. The first set of results addresses the problem of influence maximization, in which the goal is to determine the optimal group of individuals in a social network to target with an advertising campaign in order to cause a new product or technology to spread throughout the network. We then discuss an analysis of the properties of graphs that allow or prohibit the widespread propagation of trends.