Effective Big Data management and analysis poses several difficult challenges for modern database architectures. One key such challenge arises from the naturally streaming nature of big data, which mandates efficient algorithms for querying and analyzing massive, continuous data streams (that is, data that is seen only once and in a fixed order) with limited memory and CPU-time resources. Such streams arise naturally in emerging large-scale event monitoring applications; for instance, network-operations monitoring in large ISPs, where usage information from numerous sites needs to be continuously collected and analyzed for interesting trends. In addition to memory- and time-efficiency concerns, the inherently distributed nature of such applications also raises important communication-efficiency issues, making it critical to carefully optimize the use of the underlying network infrastructure. In this talk, we introduce the distributed data streaming model, and discuss some of our recent results on tracking complex queries over massive distributed streams, as well as new research directions in this space.