Big data analytics pose several challenges for modern databases. One key such challenge arises from the streaming nature of big data, which mandates efficient algorithms for querying and analyzing massive, continuous data streams with limited memory and CPU-time resources. Such streams arise naturally in emerging large-scale event monitoring applications. In addition to memory- and time-efficiency concerns, the inherently distributed nature of such applications raises important communication-efficiency issues, making it critical to carefully optimize the use of network resources. In this talk, we introduce the distributed data streaming model, and discuss some of our work on tracking complex queries over massive distributed streams, as well as new research directions in this space.