The study of the spread of influence through a social network has a long history in the social sciences. The first studies focused on the adoption of medical and agricultural innovations, later marketing researchers investigated the "word-of-mouth" diffusion process as an important mechanism by which information can reach large populations, possibly influencing public opinion, driving new product market share and brand awareness. Recently, thanks to the success of on-line social networks and microblogging platforms such as Facebook and Twitter, the phenomenon or influence exerted by users of an online social network on other users and how it propagates in the network, has attracted the interest of computer scientists and IT specialists. One of the key problems in this area is the identification of influential users, by targeting whom certain desirable outcomes can be achieved. Here, targeting could mean giving free )or price discounted) samples of a product and the desired outcome may be to get as many customers to buy the product as possible. In this talk we take a data mining perspective and we discuss what (and how) can be learned from available traces of past propagations. While doing this we provide a brief survey of some recent progresses in this area, as well as discuss the open problems.