Social influence is deeply weaved into the fabric of human society and affects every aspect of human life. Computational social influence is aimed at empowering social influence with computational tools such as modeling, algorithm design, and data mining, so as to enable influence-based applications such as viral marketing, cascade detection, etc. In this talk, I will focus on the study of influence diffusion dynamics and the influence maximization problem, which is the problem of selecting a small number of seed nodes in a social network such that their influence coverage after the influence diffusion process is maximized. I will first survey recent developments in influence maximization including scalable influence maximization and competitive influence maximization, and then introduce as an example our latest work on amphibious influence maximization, which aims at combining traditional marketing with viral marketing and addresses the technical issue of how to deal with non-submodular cases in influence maximization. I will conclude the talk with some discussions on future directions in computational social influence.