This dissertation is situated at the interface between lexical semantics, pragmatics, and cognitive linguistics. The precise aim is to work out a refined definition of polysemy and how polysemy is situated at the semantics/pragmatics interface by means of an empirical data-based investigation of the polysemy of prepositions. Prepositions have mainly been studied through a cognitive linguistic lens with image schemas and semantic networks to represent relations between their different uses or ‘senses’ (see, for instance, Brugman, 1983; Lakoff, 1987; Tyler & Evans, 2003 on over). This dissertation takes a critical approach to these past accounts, criticising in particular their methodological approaches. There are no clear definitions of a sense and of what constitutes a sense, the approaches rely solely on the researchers’ introspective judgments, and the analyses and resulting semantic networks are based on made-up examples instead of naturally occurring data. A notable exception to this is the work by Tyler and Evans (2003) who proposed methodological criteria to aid in defining a sense and separating a sense (i.e., its semantically encoded meaning) from contextual influences and inference. Despite this, their work is still based on made-up examples. This dissertation aims to build on this by consulting naturally occurring data from corpora and novels (representing a breadth of genres and topic areas) and by adopting and refining the criteria from Tyler and Evans (2003). The latter point is important in attempting to get a clearer picture of how polysemy is situated at the semantics/pragmatics interface and to answer questions such as, how many senses does/should a preposition (or polyseme in more general terms) have? Is every possible use in context a conventionalised sense? Where is the line to be drawn between a conventionalised sense and contextual influences (from the sentential context or supplied by inference)? To accomplish this, eight English prepositions are analysed using the cognitive linguistics framework with image schema configurations and semantic networks. This involves prepositions that are primarily spatial like over, under, at, and on, as well as prepositions that are primarily temporal (after) and abstract (about, by, for). For each preposition, senses are identified using the aforementioned methodological criteria, and these senses are analysed qualitatively and quantitatively. Borderline cases (i.e., non-prepositional uses) are also included in the analysis for each preposition and semantic networks are proposed as a potential mode of storage in the mental lexicon. The study also has a cross-linguistic component, where three German prepositions (translation counterparts to some of the English prepositions, namely in, an, and auf) are also analysed. The aim of this is to see if (and if so, how) polysemy is mirrored cross-linguistically and if (and where) there are overlaps in the semantic networks of different prepositions.