X-ray imaging started over a century ago. For several decades its only form was absorption radiography, in which contrast is due to local variations in beam attenuation. About forty years ago, a new form of X-ray imagery, Bragg-diffraction imaging or X-ray topography, developed into practical use. It directly reveals crystal defects in the bulk of large single crystals, and paved the way to microelectronics by leading to the growth of large, practically perfect, crystals. The advent of third-generation synchrotron radiation sources of X-rays such as ESRF and APS is now making possible, through the coherence of the X-ray beams, a novel form of radiography, in which contrast arises from phase variations across the transmitted beam, associated with optical path length differences, through Fresnel diffraction. Phase radiography and its three-dimensional companion, X-ray phase tomography, are providing new information on the mechanics of composites as well as on biological materials.