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X-ray sources are developing rapidly and their coherent output is growing correspondingly. The increased coherent flux from modern X-ray sources is being matched with an associated development in experimental methods. This article reviews the literature describing the ideas that utilize the increased brilliance from modern X-ray 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 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.