Online social networks have become an important platform for people to communicate, share knowledge and disseminate information. Given the widespread usage of social media, individuals' ideas, preferences and behavior are often influenced by their peers or friends in the social networks that they participate in. Since the last decade, influence maximization (IM) problem has been extensively adopted to model the diffusion of innovations and ideas. The purpose of IM is to select a set of k seed nodes who can influence the most individuals in the network. In this survey, we present a systematical study over the researches and future directions with respect to IM problem. We review the information diffusion models and analyze a variety of algorithms for the classic IM algorithms. We propose a taxonomy for potential readers to understand the key techniques and challenges. We also organize the milestone works in time order such that the readers of this survey can experience the research roadmap in this field. Moreover, we also categorize other application-oriented IM studies and correspondingly study each of them. What's more, we list a series of open questions as the future directions for IM-related researches, where a potential reader of this survey can easily observe what should be done next in this field.