ABSTRACT As smartphones and GPS-enabled devices proliferate, location-based services become all the more important in social networking, mobile applications, advertising, traffic monitoring, and many other domains. Managing the locations and trajectories of numerous people, vehicles, vessels, commodities, etc. must be efficient and robust, since this information must be processed online and should provide answers to users' requests in real time. In this geostreaming context, such long-running continuous queries must be repeatedly evaluated against the most recent positions relayed by moving objects; for instance, reporting which people are now moving in a specific area, or finding friends closest to the current location of a mobile user. In essence, modern processing engines must cope with huge amounts of streaming, transient, uncertain and heterogeneous spatiotemporal data, which can be characterized as big trajectory data. In this talk, we examine big data processing techniques over frequently updated locations and trajectories of moving objects. Indeed, the big data issues regarding Volume, Velocity, Variety, and Veracity also arise in this case. There is a close synergy between the established stream processing paradigm and spatiotemporal properties inherent in motion features. Taking advantage of the spatial locality and temporal timeliness that characterize each trajectory, we present methods and heuristics from our recent research results that address such problems. We highlight certain aspects of big trajectory data management: regarding Volume, we suggest single-pass algorithms that can summarize each object’s course into succinct, reliable representations; to cope with Velocity, an amnesic trajectory approximation structure may offer fast, multi-resolution synopses by dropping details from obsolete segments; detection of objects that travel together can lead to trajectory multiplexing, hence reducing the Variety inherent in raw positional data; as for Veracity, we discuss a probabilistic method for continuous range monitoring against user locations with varying degrees of uncertainty, due to privacy concerns in geosocial networking. BIOGRAPHICAL NOTE