Computational methods have revolutionized evolutionary biology. In this paper we explore the impact these methods are now having on our understanding of the forces that both affect the diversification of human languages and shape human cognition. We show how these methods can illuminate problems ranging from the nature of constraints on linguistic variation to the role that social processes play in determining the rate of linguistic change. Throughout the paper we argue that the cognitive sciences should move away from an idealized model of human cognition, to a more biologically realistic model where variation is central.Variation is the key Evolutionary scientists study variation. A key element of the Darwinian revolution was the insight that variation within species was not some superficial noise that should be stripped away to reveal the underlying species essence [1]. Variation is the signal -over evolutionary time variation within species becomes variation between species. As a legacy of the 1950s Cognitive Science movement, cognitive scientists have often thought of language on a par with vision, olfaction or memory -a human faculty with a universal organization, subject only to minor variation. But compared to animal communication systems one of the most remarkable things about human language is that there are 7000 of them, and they are culturally variable at every level of their structure, from the sound system, to the grammar, to the semantics. In this review we explore why this is, what has driven the diversification of languages, and how these processes can be systematically studied. Rather than viewing this diversity as noise distorting underlying principles, we argue that this variation is a vital resource for understanding the crucial capacity that makes us human, and that tools derived from evolutionary biology give us powerful new ways of analyzing this variation [2][3][4].Why do languages vary? Darwin [5] pondered this point, noting the curious parallels between languages and species, and indeed similar processes of speciation, drift, and adaptation can be observed in the language domain. Processes of group boundary formation account for change under demographic pressures, drift accounts for change by geographic or social isolation, and adaptation for the changes that can be observed as languages reflect the cultural uses to which they are put (with e.g. color words reflecting the technology of dye and paint [6], kinship terms the systems of marriage, residence and inheritance [7], and highly embedded sentences the growth of literacy and its specialist genres [8]).These observations are not new (although there is much recent literature providing new data and insight). What is new, however, is the recent development of highly sophisticated computational tools for exploring these processes of diversification. What these tools make possible is the meticulous inference of detailed past processes from the current diversity in all its complexity. This is time travel of a kind we could in the past onl...