Motile cilia and flagella produce regular bending waves that enable single-cell navigation due to non-planar waveforms with characteristic torsion. However, it is not known how torsion, a geometric property of the three-dimensional waveform, relates to mechanical twist deformations of the axoneme, the conserved cytoskeletal core of cilia and flagella. Here we show that axoneme twisting and torsion are coupled and that twist waves propagate along the beating axoneme of Chlamydomonas reinhardtii algae. We resolve the three-dimensional shapes of the axonemal waveform with nanometre precision at millisecond timescales using defocused dark-field microscopy and beat-cycle averaging, observing regular hetero-chiral torsion waves propagating base to tip. To investigate whether the observed torsion results from axonemal twist, we attach gold nanoparticles to axonemes and measure their cross-section rotation during beating. We find that, locally, the axonemal cross-section co-rotates with the bending plane, evidencing twist–torsion coupling. Our results demonstrate the link between shape and mechanical deformation in beating axonemes and can inform models of the dynamics of motor proteins inside the axoneme responsible for shaping the beat of motile cilia.