Energy dispersive X-ray microanalysis of thin specimens in a transmission electron microscope is a valuable method for investigating the chemistry of the nano-scale structure of rocks and minerals. This chapter summarizes first the key elements of this technique, including X-ray generation from the specimen, the detection chain and the quantification of spectra collected. The second part of the chapter is devoted to applications of the technique to extraterrestrial objects (Martian meteorites, cometary dust, primitive chondrites). Through examples, the different EDX working modes are illustrated (spot analysis, line profile, element map). Beam-damage issues are also discussed.