Focusing X-ray telescopes have been the most important factor in X-ray astronomy�s ascent to equality with optical and radio astronomy. They are the prime tool for studying thermal emission from very high temperature regions, non-thermal synchrotron radiation from very high energy particles in magnetic fields and inverse Compton scattering of lower energy photons into the X-ray band. Four missions with focusing grazing incidence X-ray telescopes based upon the Wolter 1 geometry are currently operating in space within the 0.2 to 10?keV band. Two observatory class missions have been operating since 1999 with both imaging capability and high resolution dispersive spectrometers. They are NASA�s Chandra X-ray Observatory, which has an angular resolution of 0.5 arc seconds and an area of 0.1?m2 and ESA�s XMM-Newton which has 3 co-aligned telescopes with a combined effective area of 0.43?m2 and a resolution of 15 arc seconds. The two others are Japan�s Suzaku with lower spatial resolution and non-dispersive spectroscopy and the XRT of Swift which observes and precisely positions the X-ray afterglows of gamma-ray bursts. New missions include focusing telescopes with much broader bandwidth and telescopes that will perform a new sky survey. NASA, ESA, and Japan�s space agency are collaborating in developing an observatory with very large effective area for very high energy resolution dispersive and non-dispersive spectroscopy. New technologies are required to improve upon the angular resolution of Chandra. Adaptive optics should provide modest improvement. However, orders of magnitude improvement can be achieved only by employing physical optics. Transmitting diffractive-refractive lenses are capable theoretically of achieving sub-milli arc second resolution. X-ray interferometry could in theory achieve 0.1 micro arc second resolution, which is sufficient to image the event horizon of super massive black holes at the center of nearby active galaxies. However, the physical optics systems have focal lengths in the range 103 to 104 km and cannot be realized until the technology for accurately positioned long distance formation flying between optics and detector is developed.
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