We describe in this chapter a set of statistical methods for testing cross-cultural hypotheses about correlated evolution of cultural traits. Our methods make use of phylogenies of cultures and can take into account uncertainty about what the true phylogeny is in testing hypotheses. Cross-cultural and across-species studies are conventionally called 'comparative' studies, and the statistical methods for analysing comparative data are known as comparative methods. Comparative methods comprise one of biology's most enduring sets of techniques for investigating evolution and adaptation (Harvey and Pagel 1991; Pagel 1999a). They are widely used in evolutionary biology, molecular evolution, animal behaviour, ecology and conservation.