Evolutionary approaches to cultural change are increasingly influential, and many scientists believe that a 'grand synthesis' is now in sight. The papers in this Theme Issue, which derives from a symposium held by the AHRC Centre for the Evolution of Cultural Diversity (University College London) in December 2008, focus on how the phylogenetic tree-building and network-based techniques used to estimate descent relationships in biology can be adapted to reconstruct cultural histories, where some degree of inter-societal diffusion will almost inevitably be superimposed on any deeper signal of a historical branching process. The disciplines represented include the three most purely 'cultural' fields from the four-field model of anthropology (cultural anthropology, archaeology and linguistic anthropology). In this short introduction, some context is provided from the history of anthropology, and key issues raised by the papers are highlighted.