During the past three decades, there has been a proliferation of new physical techniques for elemental analysis within a transmission electron microscope (TEM). Emphasis in analytical transmission electron microscopy (AEM) is put on the analysis of extremely small specimen volumes with high sensitivity. These physical techniques involve irradiation of the specimen with the electrons of the electron microscope in order to (i) produce a particular excitation of the elements in the specimen which can be detected by the emission of particles or of electromagnetic radiation or (ii) obtain quantitative information about the specimen by scattering or absorption of the incident electrons. In AEM, usually characteristic X-rays and electron energy losses are analyzed leading to the chemical composition of a small specimen volume. Simultaneously, information on structure and morphology of the specimen can be obtained by conventional TEM. The spatial resolution at which an electron microscope operates ranges from 0.5 nm to 10 nm and this resolution is determined by (i) the actual probe size in the AEM, (ii) the spreading of the beam within a sample, (iii) the size of the interaction region that gives rise to the detected signal and (iv) the signal-to-noise ratio of the signal. The possibilities and limitations of the techniques are elaborated for different examples which concentrate on the evaluation of structure and chemistry of interfaces in metallic and ceramic specimens. © 1990 Springer-Verlag.