This chapter provides an overview of language variation and of how formal models have been used to investigate the dynamics of language. It briefly outlines the dimensions over which language structures can vary, then explores some of the very different ways in which language change has been studied (sociolinguistics, historical linguistics, evolutionary linguistics). It describes how dynamic models of change have been successfully used in all of these fields and how they have provided insights into many aspects of language dynamics, from the properties of language change, through phylogenetic analyses of language history, to models of the cultural evolution of language.