Cilia are specialized cellular organelles that are united in structure and implicated in diverse key life processes across eukaryotes. In both unicellular and multicellular organisms, variations on the same ancestral form mediate sensing, locomotion and the production of physiological flows. As we usher in a new, more interdisciplinary era, the way we study cilia is changing. This special theme issue brings together biologists, biophysicists and mathematicians to highlight the remarkable range of systems in which motile cilia fulfil vital functions, and to inspire and define novel strategies for future research. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.