The past few decades have seen a rapid increase in the availability and use of large music corpora. However, most music corpus studies remain limited to Western music, limiting our ability to understand the diversity and unity of human music throughout the world. I argue for the potential of cross-cultural corpus studies to contribute to comparative musicological studies in domains including music classification, evolution, universals, and human history. I highlight and discuss a number of important cross-cultural corpora, including the Berlin Phonogramm-Archiv, CompMusic Project, Essen Folksong Collection, Cantometrics Project, Garland Encyclopedia of World Music, Natural History of Song, and Deep History of Music projects. In the process, I discuss the pros and cons of music notation vs. recordings, automatic vs. manual analysis, regional vs. global analysis, and associated challenges regarding choosing appropriate analysis methods that can allow meaningful comparison across cultures. I argue for the need for bigger and better global music corpora and more emphasis on integration within and beyond academia, including to domains such as the music industry and cultural heritage organizations.