Computational models have played a central role in the debate over language learnability. This article discusses how they have been used in different stances, from generative views to more recently introduced explanatory frameworks based on embodiment, cognitive development and cultural evolution. By digging into the details of certain specific models, we show how they organize, transform and rephrase defining questions about what makes language learning possible for children. Finally, we present a tentative synthesis to recast the debate using the notion of learning bias.