At first a survey of the methodic state of the art in analytical transmission electron microscopy is given. This concerns both the lateral and the analytical resolution, contrast phenomena and electron-solid interactions. The efficiency of the analytical techniques electron nanodiffraction, energy dispersive X-ray spectroscopy (EDXS), and electron energy loss spectroscopy (EELS) is discussed. The possibilities and the limitations of analytical TEM are demonstrated at cross-sections of nanometer scaled multilayers of relevant functional materials. Concentration profiles are taken from EDX and EEL spectra of Fe-Cr and Co-Cu multilayers, which are standard systems for the investigation of giant magnetoresistance (GMR). Furthermore, from the course of the electron energy loss near edge structure (ELNES) conclusions concerning the chemical bonding are possible. This will be discussed for the oxygen bonding in interface regions of the system Al2O3-TiN. The results allow to distinguish between different oxide phases in thin functional layers.