Social media platforms such as Twitter and Facebook have seen increasing adoption by people worldwide. Coupled with the habit of people to use social media for sharing their daily activities and experiences, it is not surprising that a substantial part of real-world events are well described by the online streams of status updates, posts and media content. In fact, in the case of large events, such as festivals, the number of online messages and shared content can be so high that it is very hard to get an objective view of the event. To this end, this paper presents EventSense, a social media sensing framework that can help event organizers and enthusiasts capture the pulse of large events and gain valuable insights into their impact on visitors. More specifically, EventSense enables the automatic association of online messages to entities of interest (e.g. films in the case of a film festival), the automatic discovery of topics discussed online, and the detection of sentiment (positive/negative/neutral) both at an entity level (e.g. per film) and on aggregate. In addition, the framework produces an informative social media summary of the event of interest by automatically selecting and putting together its highlights, e.g. the most discussed entities and topics, the most influential users, the evolution of the discussions' sentiment, and the most shared media and news content. A real-world case study is presented by applying EventSense on a rich dataset collected around the 53rd Thessaloniki International Film Festival.