Information for phase identification may be gathered in the electron transmission microscope with spatial resolution down to the nanometre scale. Energy dispersive X-ray and electron energy loss spectrometries are based on inelastic electron/sample interaction. They have the advantage to give a direct knowledge of the chemical nature of the atoms under the electron probe, sometimes also with valence and bonding, but concentrations are mean values over all atoms in the excited volume that may be insufficient when composition is not uniform. Moreover, X-ray absorption, electron scattering and channeling may lead to errors hard to notice and correct. Elastic interaction is observed on diffraction patterns for crystalline phases with the advantage that superimposed patterns in the case of mixtures are easily most often differentiated . It leads to phase identification via crystallographic databases. When the scale of investigation goes down to a few nanometres or tens of nanometres, indexing diffractograms of high-resolution transmission electron microscopy images is attractive, but it is often forgotten that such diffractograms are not actual diffraction patterns of the crystal itself and that lattice spacings may even be shifted by several per-cents in spheroidal nanoparticles.