More and more applications require real-time processing of heterogeneous data streams. In terms of the “Vs” of Big Data (volume, velocity, variety and veracity), they require addressing velocity and variety at the same time. Big Data solutions able to handle separately velocity and variety have been around for a while, but only Stream Reasoning approaches those two dimensions at once. Current results in the Stream Reasoning field are relevant for application areas that require to: handle massive datasets, process data streams on the fly, cope with heterogeneous incomplete and noisy data, provide reactive answers, support fine-grained information access, and integrate complex domain models. This talk starting from those requirements, frames the problem addressed by Stream Reasoning. It poses the research question and operationalise it with four simpler sub-questions. It describes how the database group of Politecnico di Milano positively answered those sub-questions in the last 7 years of research. It briefly surveys alternative approaches investigated by other research groups world wide and it elaborates on current limitations and open challenges.