Microblogs have gradually become popular platforms for users to acquire and share information with the public, which have brought a profound impact on information propagation. This paper presents a survey of predicting information propagation in microblogs. It is important to public opinion monitoring, online marketing and personalized recommendation. The paper first introduces the mechanism of information propagation, and reveals the characteristics of information propagation in microblogs through a brief overview of the qualitative research. Then, representative work is reviewed for the prediction of information propagation from three aspects including information centered prediction, user centered prediction and information-user centered prediction. The three corresponding tasks are predicting the popularity of information, predicting individual spread behaviors and predicting the path of information dissemination respectively. Next, the publicly available data sets for information propagation in microblogs are summarized. Finally, the key challenges are discussed to suggest the future research directions.