In this paper we analyse the issue of reference using spatial language and examine how the polysemy exhibited by spatial prepositions can be incorporated into semantic models for situated dialogue. After providing a brief overview of polysemy in spatial language and a review of related work, we describe an experimental study we used to collect data on a set of relevant spatial prepositions. We then establish a semantic model in which to integrate polysemy (the Baseline Prototype Model), which we test against a Simple Relation Model and a Perceptron Model. To incorporate polysemy into the baseline model we introduce two methods of identifying polysemes in grounded settings. The first is based on ‘ideal meanings’ and a modification of the ‘principled polysemy’ framework and the second is based on ‘object-specific features’. In order to compare polysemes and aid typicality judgements we then introduce a notion of ‘polyseme hierarchy’. Finally, we test the performance of the polysemy models against the Baseline Prototype Model and Perceptron Model and discuss the improvements shown by the polysemy models.