Abstract A spatio-temporal database manages spatio-temporal objects and supports corresponding query languages. Today, the term moving objects databases is used as a synonym for spatio-temporal databases managing spatial objects with a continuously changing geospatial location and/or extent. Recent advances in wireless communication, miniaturization of spatially enabled devices and global navigation satellite systems (GNSS) services have resulted in a large number of novel application domains. Applications in these novel domains (geo-sensor networks, moving objects tracking, real-time traffic analysis, etc.) process huge volumes of continuous data streams, i.e. data sets that are produced incrementally over time, rather than those available in full before the processing begins. Several data stream management systems (DSMSs) have been developed to manage this data. Since they are mainly based on a relational paradigm, they do not support geospatial data. Therefore, there is an urgent need for geospatial data stream management, ranging from real-time monitoring and alerting to long-term analysis of processed geospatial data. In this paper we present a formal framework consisting of data types and operations needed to support geospatial data in data streams. It can be used as a basis either for implementation of a completely new geospatial DSMS, or for extending available open source products and research prototypes. We leverage the work on abstract data types from spatio-temporal databases, present an implementation based on user-defined aggregate functions and illustrate embedding into an SQL-like language.