Online social media provide a platform for rapid network propagation of information at an unprecedented scale. In this paper, we study the evolution of information cascades in Twitter using a point process model of user activity. Twitter is rich with heterogenous information on users and network structure. We develop several Hawkes process models considering various properties of Twitter including conversational structure, users’ connections and general features of users including the textual information, and show how they are helpful in modeling the social network activity. Evaluation on Twitter data sets shows that incorporating richer properties improves the performance in predicting future activity of users and memes. © 2017 Association for Computing Machinery.