Apparatus for phase-contrast X-ray computed tomography using a monolithic X-ray interferometer is presented with some observational results for human breast tissues. Structures characteristic of the tissues were revealed in the phase-contrast tomograms. The procedure of image analysis consists of phase retrieval from X-ray interference patterns and tomographic image reconstruction from the retrieved phase shift. Next, feasibility of phase-contrast imaging using a two-crystal X-ray interferometer was studied aiming at in vivo observation in the future. In a preliminary study, the two-crystal X-ray interferometer was capable of generating fringes of 70% visibility using synchrotron X-rays.