Studies of language change have begun to contribute to answering several pressing questions in cognitive sciences, including the origins of human language capacity, the social construction of cognition and the mechanisms underlying culture change in general. Here, we describe recent advances within a new emerging framework for the study of language change, one that models such change as an evolutionary process among competing linguistic variants. We argue that a crucial and unifying element of this framework is the use of probabilistic, data-driven models both to infer change and to compare competing claims about social and cognitive influences on language change.