In this dissertation, I develop a novel framework to study the diffusion of urgent events through the popular social media platform—Twitter. Based on my literature review, this is the first comprehensive study on urgent event diffusion through Twitter. I observe similar diffusion patterns among different data sets and adopt the "cross prediction" mode to handle the early time prediction problem. I show that the statistics from the network of Twitter retweets can not only provide profound insights about event diffusion, but also can be used to effectively predict user influence and topic popularity. The above findings are consistent across various experiment settings. I also demonstrate that linear models consistently outperform state-of-art nonlinear ones in both user and hashtag prediction tasks, possibly implying the strong log-linear relationship between selected prediction features and the responses, which potentially could be a general phenomenon in the case of urgent event diffusion.