Over the past ten years, a subfield of GIScience has been recognized that addresses the linkage between human thought regarding geographical space, and the mechanisms for implementing these concepts in computational models. This research area has developed an identity through a series of successful international conferences and the establishment of a journal. It has also been complemented through community activities such as international standardization efforts and GIS interoperability. Historically, much of the advancement in computational methods has occurred at or close to the implementation level, as exemplified by attention to the development of spatial access methods. Significant progress has been made at the levels of spatial data models and spatial query languages, although we note the lack of a comprehensive theoretical framework comparable to the relational data model in database management systems. The difficult problems that need future research efforts are at the highly abstract level of capturing semantics of geographical information. A cognitive motivation is most promising as it shapes the focus on the users' needs and points of view, rather than on efficiency as in the case of a bottom-up system design. We also identify the need for new research in fields, models of qualitative spatial information, temporal aspects, knowledge discovery, and the integration of GIS with database management systems.