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X-ray sources are developing rapidly and their coherent output is growing extremely rapidly. The increased coherent flux from modern X-ray sources is being matched with an associated rapid development in experimental methods. This article reviews the literature describing the ideas that utilise the increased brilliance from modern Xray sources. It explores how ideas in coherent X-ray science are leading to developments in other areas, and vice versa. The article describes measurements of coherence properties and uses this discussion as a base from which to describe partially-coherent diffraction and X-ray phase contrast imaging, with its applications in materials science, engineering and medicine. Coherent diffraction imaging methods are reviewed along with associated experiments in materials science. Proposals for experiments to be performed with the new X-ray free-electron-lasers are briefly discussed. The literature on X-ray photon correlation spectroscopy is described and the features it has in common with other coherent X-ray methods are identified. Many of the ideas used in the coherent X-ray literature have their origins in the optical and electron communities and these connections are explored. A review of the areas in which ideas from coherent X-ray methods are contributing to methods for the neutron, electron and optical communities is presented.

Very high-resolution X-ray imaging has been the subject of considerable research in the last few decades. However the spatial resolution of these methods is limited by the quality of the X-ray optics that can be manufactured. More recently, lensless Xray imaging has emerged as a powerful approach that is able to circumvent the limitations on X-ray optics. A number of classes of lensless X-ray imaging have been developed, many with origins in other forms of optics, and the key progress to date is here reviewed. We describe applications of the methods in imaging for biology and materials science, as well as the prospect for the imaging of single molecules using X-ray free electron lasers.X-ray crystallography has a record of extraordinary achievement in science and its impact on the biological sciences has been immense. From its inception crystallography has numerically synthesized three-dimensional atomic-resolution images of molecules from the beams diffracted by their crystal forms. However, it was not until the influence of macromolecular crystallography was being fully realized that a prominent crystallographer, David Sayre, proposed 1 that the methods of crystallography might be