In this paper human experience and perception of phenomena and relations in space are studied. This focus is in contrast to previous work where space and spatial relations were examined as objective phenomena of the world. This study leads in turn to a goal: to identify models of space that can be used both in cognitive science and in the design and implementation of geographic information systems (GISs). Experiential models of the world are based on sensorimotor and visual experiences with environments, and form in individual minds, as the associated bodies and senses experience their worlds. Formal models consist of axioms expressed in a formal language, together with mathematical rules to infer conclusions from these axioms. In this paper we will review both types of models, considering each to be an abstraction of the same ‘real world’. The review of experiential models is based primarily on recent developments in cognitive science, expounded by Rosch, Johnson, Talmy, and especially Lakoff. In these models it is suggested that perception and cognition are driven by image-schemata and other mental models, often language-based. Cross-cultural variations are admitted and even emphasized. The ways in which people interact with small-scale (‘tabletop’) spaces filled with everyday objects are in sharp contrast to the ways in which they experience geographic (large-scale) spaces during wayfinding and other spatial activities. We then address the issue of the ‘objective’ geometry of geographic space. If objectivity is defined by measurement, this leads to a surveyor's view and a near-Euclidean geometry. These models are then related to issues in the design of GISs. To be implemented on digital computers, geometric concepts and models must be formalized. The idea of a formal geometry of natural language is discussed and some aspects of it are presented. Formalizing the links between cognitive categories and models on the one hand and between geometry and computer representations on the other are key elements in the research agenda.