X-ray detectors for imaging with a spatial resolution in the micrometer and submicrometer range have been developed at synchrotron radiation sources since 1996. The detectors consist of a scintillator, a light microscopy optic and a charge-coupled device (CCD). The scintillator converts part of the X-ray stopped by a material into a visible-light image which is projected onto the CCD by the light optics. A resolution of 0.5 microm FWHM has been achieved using a 1 microm-thick europium-doped Lu3Al5O12 film. The detective quantum efficiency of the detector is mainly limited by the low absorption of X-rays in the thin layer of the scintillator. To increase the absorption, and therefore reduce the exposure time, new scintillators (Lu2O3:Eu3+, Gd2O3:Eu3+, Lu2SiO5:Ce, Gd3Ga5O12:Eu3+, CdWO4) have been investigated. These were fabricated using sol-gel and liquid-phase epitaxy processes. Finally, the first fast microtomography experiment including radiation hardness of the optic is shown. This detector uses a high-intensity white beam with 60 keV effective energy and a fast CCD camera at up to 60 frames s(-1).