As computers become faster and more powerful, it is increasingly possible to provide better solutions to many geographical problems by developing new, computationally dependent tools for analysis and modelling. The term ‘geocomputation’ has been coined to describe the development and application of these tools. There are already indications of a significant increase in the number of research activities and funding opportunities that involve leading-edge computer-based tools and techniques, and geocomputational techniques are poised to provide novel solutions to a mix of old and new problems in spatial analysis. An increasingly important component of much geocomputational analysis is the use of GIs. These provide the platform for data storage, abstraction, analysis, and visualization. However, although GIS have successfully created an infrastructure for gathering, storing, and manipulating spatial information, these technologies are often deficient when it come to analysis and modelling. Geography needs to use, process, and add value to the massive amount of spatial information now available and researchers in GIS are well-poised to exploit the impact of new technologies for performing these tasks. The leading parallel supercomputers are today running at speeds a few thousand times faster than those provided by even the fastest personal computers and offer memory spaces soon expected to reach a Terabyte. The papers in this special issue of Tranructions in GZS demonstrate the link between computational power and GIs. They were presented at the First International Conference on Geocomputation held at the University of Leeds in 1996. The principal objective of the conference was to bring together various emergent, computer-oriented activities for the analysis and modelling of spatial data. The paper by Brookes, for example, examines the problem of identifying optimal locations of facilities on raster maps when the facilities are larger than the cell size used in the raster. A genetic algorithm is described which searches for optimal or near-optimal clusters of cells and then employs a raster GIS to evaluate the utility scores for these clusters. The results suggest that the genetic algorithm can find good solutions to locational problems when exhaustive search methods are impractical. Park and Wagner investigate a coupling of cellular automata and GIS in which the cellular automata act as an analytical engine for the GIs. Examples given on spatial diffusion and spatiotemporal processes show how dynamic spatial modelling can be handled within a GIs. Lilburne et al address the interesting issue of interoperability and GIs. As we demand more and more of GIs, particularly in the arena of spatial analysis, the question of where to draw the balance between one all-embracing GIS and the establishment of an increasing number of flexible interfaces to other systems arises. Interoperability is an attempt to recognize that some middle ground might provide the optimal future for GIs. In two very different papers, Takeyama describes his vision of Geo-Algebra to facilitate geocomputational modelling within a GIS while