In learning the meanings of words, children are guided by a set of constraints that give privilege to some potential meanings over others. These word-learning constraints are sometimes viewed as part of a specifically linguistic endowment. However, several recent computational models suggest concretely how word-learning - constraints included - might emerge from more general aspects of cognition, such as associative learning, attention and rational inference. This article reviews these models, highlighting the link between general cognitive forces and the word-learning they subserve. Ultimately, these cognitive forces might leave their mark not just on language learning, but also on language itself: in constraining the space of possible meanings, they place limits on cross-linguistic semantic variation.