Computational methods derived from evolutionary biology are increasingly being applied to the study of cultural evolution. This is particularly the case in studies of language evolution, where phylogenetic methods have recently been used to test hy- potheses about divergence dates, rates of lexical change, borrowing, and putative lan- guage universals. This chapter outlines three new and related questions that could be productively tackled with computational phylogenetic methods: What drives language diversification? What drives differences in the rate of linguistic change (disparity)? Can we identify cultural and linguistic homelands?