Existing theories of word learning largely focus on a learner's ability to learn a single meaning for a word despite the fact that many words have multiple meanings. Several computational models of cross-situational word learning have been proposed to explain how words are learned, but it is unknown to what extent they can learn ambiguous words with multiple meanings. Here, we present an experiment showing that adult learners are able to learn multiple meanings of novel ambiguous words in a cross-situational word learning paradigm, and are especially good at doing so when the meanings of the words are related (polysemous) rather than unrelated (homophonous). We evaluated the ability of ten different computational models of cross-situational word learning to explain the empirical data, and none were able to learn the ambiguous words as successfully as the adult learners. Moreover, because these computational models do not represent any semantic information, they are in principle unable to replicate the key difference between polysemous and homophonous word learning found in the study.