The concept of cultural evolution was fundamental to the foundation of academic musicology and the subfield of comparative musicology, but largely disappeared from discussion after World War II despite a recent resurgence of interest in cultural evolution in other fields. I draw on recent advances in the scientific understanding of cultural evolution to clarify persistent misconceptions about the roles of genes and progress in musical evolution, and review literature relevant to musical evolution ranging from macroevolution of global songstyle to microevolution of tune families. I also address criticisms regarding issues of musical agency, meaning, and reductionism, and highlight potential applications including music education and copyright. While cultural evolution will never explain all aspects of music, it offers a useful theoretical framework for understanding diversity and change in the world's music.