The influence maximization problem, which asks for a small node set of maximum influence, is a key algorithmic problem in social influence analysis, and has been extensively studied over the past decade. It has wide applications to viral marketing, outbreak detection, rumor monitoring, etc. Meanwhile, there are several related problems, such as the profit maximization problem, etc. In most of the known results, the submodularity of the influence function plays a vital role for designing efficient and theoretical bounded solutions. In this talk, I will show some new results obtained by our group.