Since the middle of the 1990s, X-ray phase imaging including phase tomography has been attracting increasing attention. The advantage of X-ray phase imaging is that an extremely high sensitivity is achieved for weak-absorbing materials, such as biological soft tissues, which generate a poor contrast by conventional methods. Medical and biological imaging is the main target of X-ray phase imaging, and several trials using synchrotron radiation sources and laboratory sources have been made. Measuring and controlling the X-ray phase are also significant for X-ray microscopy with a high spatial resolution, and innovative techniques are attracting intense interest. The progress of X-ray phase imaging is supported by the developments in X-ray sources such as third-generation synchrotron radiation sources, optical elements, and image detectors. This article describes the advantages of using X-ray phase information and reviews various techniques studied for X-ray phase imaging.