The principle of unconventional holography, called coherence holography, is proposed and experimentally demonstrated for the first time. An object recorded in a hologram is reconstructed as the three-dimensional distribution of a complex spatial coherence function, rather than as the complex amplitude distribution of the optical field itself that usually represents the reconstructed image in conventional holography. A simple optical geometry for the direct visualization of the reconstructed coherence image is proposed, along with the experimental results validating the proposed principle. Coherence holography is shown to be applicable to optical coherence tomography and profilometry.