By now, personal life has been invaded by online social networks (OSNs) everywhere. They intend to move more and more offline lives to online social networks. Therefore, online social networks can reflect the structure of offline human society. A piece of information can be exchanged or diffused between individuals in social networks. From this diffusion process, lots of latent information can be mined. It can be used for market predicting, rumor controlling, and opinion monitoring among other things. However, the research of these applications depends on the diffusion models and methods. For this reason, we survey various information diffusion models from recent decades. From a research process view, we divide the diffusion models into two categories-explanatory models and predictive models-in which the former includes epidemics and influence models and the latter includes independent cascade, linear threshold, and game theory models. The purpose of this paper is to investigate the research methods and techniques, and compare them according to the above categories. The whole research structure of the information diffusion models based on our view is given. There is a discussion at the end of each section, detailing related models that are mentioned in the literature. We conclude that these two models are not independent, they always complement each other. Finally, the issues of the social networks research are discussed and summarized, and directions for future study are proposed.