The self-imaging phenomenon referred to as the Talbot effect in the field of optics was discovered by H.F. Talbot in the 1830s, and is now widely used for imaging using not only visible light but also X-rays, electrons, neutrons, and matter waves. In this review, the author introduces the current progress being made in hard-X-ray imaging microscopy based on the self-imaging phenomenon. Hard-X-ray imaging microscopy is a promising technique for non-destructively visualizing internal structures in specimens with a spatial resolution up to a few tens of nanometers. The use of the self-imaging phenomenon makes it possible to realize highly sensitive phase-contrast X-ray imaging microscopes. These approaches have several advantages over conventional X-ray imaging microscopes, including the widely used Zernike X-ray phase-contrast microscopes, and can provide a powerful way of quantitative visualization with a high spatial resolution and a high sensitivity even for thick specimens.