This review is devoted to a comparative description of the methods for forming X-ray phase-con- trast images of weakly absorbing (phase) objects. These include the crystal interferometer method, the Talbot interferometer method, diffraction-enhanced X-ray imaging, and the in-line method. The potential of their practical application in various fields of science and technology is discussed. The publications on the devel- opment and optimization of X-ray phase-contrast methods and the experimental study of phase objects are analyzed.