Social networks now play a central role for sharing information and discussing different types of events. The way information spreads in such networks has often been compared to the way innovations spread in marketing or viruses spread in populations. As such, two of the more popular information diffusion models, the IC (Independent Cascade) and the LT (Linear Threshold) models, can be seen as instances of the standard SI (Susceptible-Infectious) family used in epidemiology. However, such models usually fail to account for important characteristics of the users sharing and diffusing information in social networks, namely the interest of the users in the information being disseminated and their willingness to diffuse a piece of information. After a presentation of the standard information diffusion models, we will introduce a new generation of models, referred to as "user-centric", which provide a more realistic modeling of how information spreads in social networks. We will furthermore explicit the differences between all these models along several dimensions (relation to percolation, influence maximization problem) and will illustrate the behavior of these models on both synthetic and real datasets.