Diffractive X-ray telescopes using zone plates, phase Fresnel lenses, or related optical elements have the potential to provide astronomers with true imaging capability with resolution several orders of magnitude better than available in any other waveband. Lenses that would be relatively easy to fabricate could have an angular resolution of the order of microarcseconds or even better, that would allow, for example, imaging of the distorted spacetime in the immediate vicinity of the supermassive black holes in the center of active galaxies What then is precluding their immediate adoption? Extremely long focal lengths, very limited bandwidth, and difficulty stabilizing the image are the main problems. The history and status of the development of such lenses is reviewed here and the prospects for managing the challenges that they present are discussed.
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