The deluge of digital information in our daily life -- from user-generated content, such as microblogs and scientific papers, to online business, such as viral marketing and advertising -- offers unprecedented opportunities to explore and exploit the trajectories and structures of the evolution of information cascades. Abundant research efforts, both academic and industrial, have aimed to reach a better understanding of the mechanisms driving the spread of information and quantifying the outcome of information diffusion. This article presents a comprehensive review and categorization of information popularity prediction methods, from feature engineering and stochastic processes, through graph representation, to deep learning-based approaches. Specifically, we first formally define different types of information cascades and summarize the perspectives of existing studies. We then present a taxonomy that categorizes existing works into the aforementioned three main groups as well as the main subclasses in each group, and we systematically review cutting-edge research work. Finally, we summarize the pros and cons of existing research efforts and outline the open challenges and opportunities in this field.
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