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 micro-arc-seconds or
even better, that would allow, for example, imaging of the distorted space-
time in the immediate vicinity of the super-massive 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.Comment: 46 pages, 15 figures, invited review paper to be published in a
special issue on "X-Ray Focusing: Techniques and Applications" of the online
journal "X-Ray Optics & Instrumentation
