The ongoing rapid expansion of the Word Wide Web (WWW) greatly increases the information of effective transmission from heterogeneous individuals to various systems. Extensive research for information diffusion is introduced by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and empirical studies, unification and comparison of different theories and approaches are lacking, which impedes further advances. In this article, we review recent developments in information diffusion and discuss the major challenges. We compare and evaluate available models and algorithms to respectively investigate their physical roles and optimization designs. Potential impacts and future directions are discussed. We emphasize that information diffusion has great scientific depth and combines diverse research fields which makes it interesting for physicists as well as interdisciplinary researchers.