In this talk, we present an event-based Epidemic Intelligence (EI) system framework leveraging social media data, e.g., Twitter messages (or tweets) for providing public health officials the necessary tools to survey and sift through relevant information, namely, disease outbreak events. There exist three main research challenges in gathering epidemic intelligence from social media streams: 1) dynamic classification to enable message filtering, 2) signal generation producing reliable warnings based on observed term frequency changes in the filtered messages, and 3) providing search and recommendation functionalities to domain experts, for better assessment of the potential outbreak threats associated with the generated signals. We outline possible approaches to solve these important challenges as well as discuss areas where further research is required. The objective is to provide guidance for similar endeavors, and to give prospective event-based Epidemic Intelligence system builders a more realistic view on the benefits and issues of social media stream analysis.