Theory and experiment are presented to show that an interface between two soft materials under compression can form creases, a type of bifurcation distinct from wrinkles. While creases bifurcate from a state of flat interface by a deformation localized in space and large in amplitude, wrinkles bifurcate from a state of flat interface by a deformation nonlocal in space and infinitesimal in amplitude. The interfacial creases set in at a lower critical compression than interfacial wrinkles, but higher than surface creases. The condition for the onset of interfacial creases is scale-free, and is calculated in terms of elastic moduli, pre-strains and applied strains.