For more than a century, the blue structural colours of mammalian skin have been hypothesized to be produced by incoherent, Rayleigh or Tyndall scattering. We investigated the colour, anatomy, nanostructure and biophysics of structurally coloured skin from two species of primates - mandrill (Mandrillus sphinx) and vervet monkey (Cercopithecus aethiops) - and two species of marsupials - mouse opossum (Marmosa mexicana) and wooly opossum (Caluromys derbianus). We used two-dimensional (2-D) Fourier analysis of transmission electron micrographs (TEMs) of the collagen arrays in the primate tissues to test whether these structural colours are produced by incoherent or coherent scattering (i.e. constructive interference). The structural colours in Mandrillus rump and facial skin and Cercopithecus scrotum are produced by coherent scattering by quasi-ordered arrays of parallel dermal collagen fibres. The 2-D Fourier power spectra of the collagen arrays from Mandrillus and Cercopithecus reveal ring-shaped distributions of Fourier power at intermediate spatial frequencies, demonstrating a substantial nanostructure of the appropriate spatial frequency to produce the observed blue hues by coherent scattering alone. The Fourier power spectra and the observed reflectance spectra falsify assumptions and predictions of the incoherent, Rayleigh scattering hypothesis. Samples of blue Marmosa and Caluromys scrotum conform generally to the anatomy seen in Mandrillus and Cercopithecus but were not sufficiently well preserved to conduct numerical analyses. Colour-producing collagen arrays in mammals have evolved multiple times independently within the two clades of mammals known to have trichromatic colour vision. Mammalian colour-producing collagen arrays are anatomically and mechanistically identical to structures that have evolved convergently in the dermis of many lineages of birds, the tapetum of some mammals and the cornea of some fishes. These collagen arrays constitute quasi-ordered 2-D photonic crystals.