Ever since the Naming Game, agent-based modelling has beautifully illustrated how shared and complex linguistic conventions could emerge out of multiple inter-speaker interactions sharing communication goals. However, how a community can switch from one linguistic convention to another – and therefore enact a language change – has remained troublesome, and usually require additional mechanisms: a selective advantage of the new variant, a change endorsed by an influential sub-community, or an amplification of ongoing trends. What has been neglected, however, is that this sociolinguistic account does not necessarily map with the available evidence of the change – namely, the frequency of use as recorded in diachronic corpora. In this talk, I will review this evidence on actual case studies, and introduce the model of language change I developed during my PhD. This model focuses not on social interactions, but on the cognitive organization of language, which is assumed to drive the change. I will then discuss the limitations of this model, and how it can be expanded in the future, especially to be reconciled with a sociolinguistic account.