Many physical phenomena create colour: spectrally selective light absorption by pigments and dyes(1,2), material-specific optical dispersion3 and light interference(4-11) in micrometre-scale and nanometre-scale periodic structures(12-17). In addition, scattering, diffraction and interference mechanisms are inherent to spherical droplets(18), which contribute to atmospheric phenomena such as glories, coronas and rainbows(19). Here we describe a previously unrecognized mechanism for creating iridescent structural colour with large angular spectral separation. Light travelling along different trajectories of total internal reflection at a concave optical interface can interfere to generate brilliant patterns of colour. The effect is generated at interfaces with dimensions that are orders of magnitude larger than the wavelength of visible light and is readily observed in systems as simple as water drops condensed on a transparent substrate. We also exploit this phenomenon in complex systems, including multiphase droplets, three-dimensional patterned polymer surfaces and solid microparticles, to create patterns of iridescent colour that are consistent with theoretical predictions. Such controllable structural colouration is straightforward to generate at microscale interfaces, so we expect that the design principles and predictive theory outlined here will be of interest both for fundamental exploration in optics and for application in functional colloidal inks and paints, displays and sensors.