Social media have become a primary communication channel among people and are continuously overwhelmed by huge volumes of User Generated Content. This is especially true in the aftermath of unpredictable disasters, when users report facts, descriptions and photos of the unfolding event. This material contains actionable information that can greatly help rescuers to achieve a better response to crises, but its volume and variety render manual processing unfeasible. This paper reports the experience we gained from developing and using a web-enabled system for the online detection and monitoring of unpredictable events such as earthquakes and floods. The system captures selected message streams from Twitter and offers decision support functionalities for acquiring situational awareness from textual content and for quantifying the impact of disasters. The software architecture of the system is described and the approaches adopted for messages filtering, emergency detection and emergency monitoring are discussed. For each module, the results of real-world experiments are reported. The modular design makes the system easy configurable and allowed us to conduct experiments on different crises, including Emilia earthquake in 2012 and Genoa flood in 2014. Finally, some possible functionalities relying on the analysis of multimedia information are introduced.