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Although matriliny and matrilocality are relatively rare in contemporary human populations, these female-based descent and residence systems are present in different cultural contexts and across the globe. Previous research has generated numerous hypotheses about which cultural traits are associated with the stability or loss of matrilineal descent. In addition, several studies have examined matrilineal descent with phylogenetic analyses; however, the use of language phylogenies has restricted these analyses to comparisons within a single language family, often confined to a single continent. Cross-cultural comparisons are particularly informative when they account for the relationships between widely distributed populations, as opposed to treating each population as an independent sample or focusing on a single region. Here, we study the evolution of descent systems on a worldwide scale. First, we test for significant associations between matriliny and numerous cultural traits that have been theoretically associated with its stability or loss, such as subsistence strategy, animal domestication, mating system, residence pattern, wealth transfer and property succession. In addition, by combining genetic and linguistic information to build a global supertree that includes 16 matrilineal populations, we also perform phylogenetically controlled analyses to assess the patterns of correlated evolution between descent and other traits: for example, does a change in subsistence strategy generally predict a shift in the rules of descent, or do these transitions happen independently? These analyses enable a worldwide perspective on the pattern and process of the evolution of matriliny and matrilocality. This article is part of the theme issue ‘The evolution of female-biased kinship in humans and other mammals’.