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.