The traditional electrochemical techniques are based on the measurement of current and potential, and, in the case of liquid electrodes, of the surface tension. While such measurements can be very precise, they give no direct information on the microscopic structure of the electrochemical interface. In this chapter we treat several methods which can provide such information. None of them is endemic to electrochemistry; they are mostly skillful adaptations of techniques developed in other branches of physics and chemistry. The scanning tunneling microscope (STM) is an excellent device to obtain topographic images of an electrode surface . The principal part of this apparatus is a metal tip with a very fine point, which can be moved in all three directions of space with the aid of piezoelectric crystals. All but the very end of the tip is insulated from the solution in order to avoid tip currents due to unwanted electrochemical reactions. The tip is brought very close, up to a few Ångstroms, to the electrode surface. When a potential bias ΔV, usually of the order of a few hundred millivolts, is applied between the electrode and the tip, the electrons can tunnel through the thin intervening layer of solution, and a tunneling current is observed. The situation is illustrated in Fig. 15.2: A potential energy barrier exists between the tip and the substrate. Application of a bias potential shifts the two Fermi levels of the tip and of the substrate. Electrons can tunnel from the metal with the higher Fermi level through the barrier to empty states on the other metal. Roughly speaking, electrons with energies between the two Fermi levels can be transferred. A detailed calculation shows that the current is proportional to the electronic density of states at the Fermi level of the substrate. The tip is moved slowly in the yz direction parallel to the metal surface, and simultaneously the distance x from the electrode is adjusted in such a way that the tunneling current is constant (constant-current mode).