Rapidly extracting business value out of Big Data that stream in corporate data centres requires continuous analysis of massive, high-speed data while they are still in motion. So challenging a goal entails that analytics should be performed in memory with a single pass over these data. In this chapter, we outline the challenges of Big streaming Data analysis for deriving real-time, online answers to application inquiries. We review approaches, architectures and systems designed to address these challenges and report on our own progress within the scope of the EU H2020 project INFORE. We showcase INFORE into a real-world use case from the maritime domain and further discuss future research and development directions.