Social media channels such as Twitter have emerged as popular platforms for crowds to respond to public events such as speeches, sports and debates. While this promises tremendous opportunities to understand and make sense of the reception of an event from the social media, the promises come entwined with significant technical challenges. In particular, given an event and an associated large scale collection of tweets, we need approaches to effectively align tweets and the parts of the event they refer to. This in turn raises questions about how to segment the event into smaller yet meaningful parts, and how to figure out whether a tweet is a general one about the entire event or specific one aimed at a particular segment of the event. In this work, we present ET-LDA, an effective method for aligning an event and its tweets through joint statistical modeling of topical influences from the events and their associated tweets. The model enables the automatic segmentation of the events and the characterization of tweets into two categories: (1) episodic tweets that respond specifically to the content in the segments of the events, and (2) steady tweets that respond generally about the events. We present an efficient inference method for this model, and a comprehensive evaluation of its effectiveness over existing methods. In particular, through a user study, we demonstrate that users find the topics, the segments, the alignment, and the episodic tweets discovered by ET-LDA to be of higher quality and more interesting as compared to the state-of-the-art, with improvements in the range of 18-41%.