This paper outlines four specific problems that appear to represent considerable obstacles to the development of visualisation strategies for use within the domain of geography and the Earth sciences. These are: (1) the speed of graphical rendering, (2) the management of perceptual anomalies due to visual combination effects, (3) the vast range of potential approaches and mappings (the complexity of the visual assignment process), and (4) the orientation of the user into an artificial or virtual reality. Each problem is discussed in terms of the visualisation of geographical data for the purpose of exploratory visual analysis. The specific underlying research issues and questions are described, with particular emphasis to how these relate to the geographical domain. Where possible, some potential solutions are suggested. Specific examples of geographical data visualisation are given to substantiate the arguments presented. The discussion highlights the need for further research in a number of key areas, and stresses the weaknesses of current visualisation theory and technology when applied to non-trivial geographical datasets.