An increasing number of applications for dialogue systems presuppose an ability to deal appropriately with space. Dialogues with assistance systems, intelligent mobility devices and navigation systems all commonly involve the use of spatial language. For smooth interaction, this spatial language cannot be interpreted 'in the abstract'-it must instead be related directly to a user's physical location, orientation, goals and needs and be embedded appropriately in a system's interaction. This is far from straightforward. The situated interpretation of natural language concerning space, spatial relationships and spatial activities represents an unsolved challenge at this time. Despite extensive work on spatial language involving many disciplines, there are no generally accepted accounts that provide support for the kind of flexible language use observed in real human-human spatial dialogues. In this paper, I review some recent approaches to the semantics for natural language expressions concerning space in order to motivate a two-level semantic-based approach to the interpretation of spatial language. This draws on a new combination of natural language processing and principles of ontological engineering and stands as a foundation for more sophisticated and natural dialogue system behavior where spatial information is involved.