We present TweetMotif, an exploratory search application for Twitter. Unlike traditional approaches to information retrieval, which present a simple list of messages, TweetMotif groups messages by frequent significant terms -- a result set's subtopics -- which facilitate navigation and drilldown through a faceted search interface. The topic extraction system is based on syntactic filtering, language modeling, near-duplicate detection, and set cover heuristics. We have used TweetMotif to deflate rumors, uncover scams, summarize sentiment, and track political protests in real-time. A demo of TweetMotif, plus its source code, is available at http://tweetmotif.com.