Most words in English are ambiguous between different interpretations; words can mean different things in different contexts. We investigate the implications of different types of semantic ambiguity for connectionist models of word recognition. We present a model in which there is competition to activate distributed semantic representations. The model performs well on the task of retrieving the different meanings of ambiguous words, and is able to simulate data reported by Rodd, Gaskell, and Marslen-Wilson [J. Mem. Lang. 46 (2002) 245] on how semantic ambiguity affects lexical decision performance. In particular, the network shows a disadvantage for words with multiple unrelated meanings (e.g., "bark") that coexists with a benefit for words with multiple related word senses (e.g., "twist"). The ambiguity disadvantage arises because of interference between the different meanings, while the sense benefit arises because of differences in the structure of the attractor basins formed during learning. Words with few senses develop deep, narrow attractor basins, while words with many senses develop shallow, broad basins. We conclude that the mental representations of word meanings can be modelled as stable states within a high-dimensional semantic space, and that variations in the meanings of words shape the landscape of this space.