We present new schemes for a next-generation X-ray telescope for the energy range between approximately 1 and 10 keV providing an angular resolution of at least 1 milli-arcsec. Its technology will be based on diffractive transmission optics, e.g. Fresnel zone plates and their derivatives. Beside near-diffraction limited imaging, these devices hold the potential of a large collecting area well beyond 10 square meters at a simple and lightweight construction, compared to conventional mirror telescopes. However, there are drawbacks. Firstly the intrinsically long focal lengths do require separation and precise
formation flight of lens and detector spacecraft. Accordingly, techniques will be discussed for relative stabilization on the one hand and possibilities to reduce focal length and thus lever arm on the other hand. For this purpose, large arrays of small, independent lenses might offer a notable perspective. Secondly, diffractive optics
feature severe focal length dispersion which has to be accepted using narrow-band spectral selection or-better-should be corrected over a practicable wide energy range. In the hard X-ray regime, hybrid lens devices made of beryllium, lithium or plastics like polycarbonate will be an appropriate solution for a fixed energy, while tunable systems with variable correction lenses possess-in principle-the capability for dispersion compensation in the soft X-ray region, too. An overview on the science case of milli-arcsec X-ray imaging will conclude the contribution. We show that significant new insights in astrophysical processes are expected just at and beyond this angular scale and give examples from X-ray binaries over AGN's up to gamma-ray bursts.