This paper outlines an argument that the meaning of spatial terms depends critically upon our mental models of space. We argue that such models capture the functional geometry of spatial scenes to represent various control relations between the objects in the scene. The discussion centres around two analyses. First, an analysis of the spatial descriptions taken from task oriented dialogue, which seem to reflect a number of distinct mental models of the same visual scene, and secondly an analysis of simple English spatial prepositions. We argue that these prepositions express control relations rather than simple spatial relations and depend for their interpretation on the model of space assumed by speaker and listener. This analysis suggests that mental models whould be seen as interfaces between the language and the world of discourse rather than simply surrogates for that world.