The goal of this work is to present the current state of the X-ray Fluorescence Computed Microtomography. The advantages of both the experimental techniques and the data processing (the ESRF ID22 beamline facilities ) are considered. The latter one includes the spectra treatment, reconstruction of the atomic density distribution function of the element under consideration and/or calculation of the element effective concentration map and calculation of the element ratio maps. Possible ways of estimating the space resolution and the accuracy are discussed. Results of the tomographic investigation of the NWA817 meteorite micro-grain are presented.