Social media channels such as Twitter have emerged as platforms for crowds to respond to public and televised events such as speeches and debates. However, the very large volume of responses presents challenges for attempts to extract sense from them. In this work, we present an analytical method based on joint statistical modeling of topical influences from the events and associated Twitter feeds. The model enables the auto-segmentation of the events and the characterization of tweets into two categories: (1) episodic tweets that respond specifically to the content in the segmentsof the events, and (2) steady tweets that respond generally about the events. By applying our method to two large sets of tweets in response to President Obama's speech on the Middle East in May 2011 and a Republican Primary debate in September 2011, we present what these tweets were about. We also reveal the nature and magnitude of the influences of the event on the tweets over its timeline. In a user study, we further show that users find the topics and the episodic tweets discovered by our method to be of higher quality and more interesting as compared to the state-of-the-art, with improvements in the range of 18-41%.