Broadband Dielectric Spectroscopy as one of the major tools in molecular physics, benefits from the extraordinary advantage that its sensitivity increases with decreasing thickness of a sample capacitor and hence with a decreasing amount of sample material. This enables one, for instance, to carry out broadband spectroscopic measurements on quasi-isolated polymer coils in nano-structured capacitor arrangements having thicknesses as small as 10 nm. It is demonstrated that for polymers like

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... c polystyrene (PS) or poly-2-vinyl-pyridine (P2VP), the dynamic glass transition can be measured for (averaged) sample thickness as small as ~ 2 nm in a wide spectral range (10 mHz to 10 MHz) and temperature interval (150 K to 350 K). No shift of the mean relaxation rate and no broadening of the relaxation time distribution function are found compared to the bulk liquid. Electrode polarization is a ubiquitous phenomenon that takes place at the interface between a metal and an ionic conductor. A quantitative theory is presented, which enables one to deduce from its characteristic frequency, temperature and concentration dependencies -by use of a novel formula -the bulk conductivity of the ion conducting liquid under study. It is shown that the electrical relaxation processes take place within a nanometric layer at the (ionic conductor/metal) interface.