We study social influence from a topic modeling perspective. We introduce novel topic-aware influence-driven propagation models that experimentally result to be more accurate in describing real-world cascades than the standard propagation models studied in the literature. In particular, we first propose simple topic-aware extensions of the well-known Independent Cascade and Linear Threshold models. Next, we propose a different approach explicitly modeling authoritativeness, influence and relevance under a topic-aware perspective. We devise methods to learn the parameters of the models from a dataset of past propagations. Our experimentation confirms the high accuracy of the proposed models and learning schemes.