Presentation at UMAP, held in Montreal, July 2012. Our research goal is to provide a better understanding of how users engage with online services, and how to measure this engagement. We should not speak of one main approach to measure user engagement – e.g. through one fixed set of metrics – because engagement depends on the online services at hand. Instead, we should be talking of models of user engagement. As a first step, we analyzed a number of online services, and show that it is possible to derive effectively simple models of user engagement, for example, accounting for user types and temporal aspects. This paper provides initial insights into engagement patterns, allowing for a better understanding of the important characteristics of how users repeatedly interact with a service or group of services. This work was done in collaboration with Mounia Lalmas, Georges Dupret, Elad Yom-Tov and Ricardo Baeza-Yates.