In recent years, large effort has been put into the development and characterization of new colossal-ε' materials. For example, the recent discovery (1,2) of "colossal" values of the dielectric constant, ε', up to about 10 5 in CaCu 3 Ti 4 O 12 (CCTO) has aroused tremendous interest and a huge number of publications deals with its investigation and optimization. Aside of the extensively investigated CCTO, there are also some reports of other colossal-ε' materials (e.g., refs. (3,4,5,6,7)), mainly transition metal oxides. While there is no clear definition, the term "colossal" typically denotes values of ε' > 10 4 . Such materials are very appealing for the further miniaturization of capacitive components in electronic devices and also in giant capacitors that may replace batteries for energy storage.Of course, colossal dielectric constants are also found in ferroelectrics where close to the phase transition very large values are reached. However, ferroelectrics are characterized by a strong temperature dependence of ε' around their critical temperature, which restricts their applicability. In contrast, CCTO and other materials stand out due to their colossal-ε' values being nearly constant over a broad temperature range around room temperature. But in all these materials a strong frequency dependence is observed, revealing the signature of relaxational contributions, namely a steplike decrease of ε' above a certain, temperaturedependent frequency, accompanied by a peak in the dielectric loss. Intrinsic relaxations are commonly observed, e.g., in materials containing dipolar molecules, which reorient in accord with the ac field at low frequencies, but cannot follow at high frequencies. However, the extensive investigations of CCTO, have quite clearly revealed that the observed relaxation features are due to a nonintrinsic effect, termed Maxwell-Wagner (MW) relaxation (8,9,10). It arises from heterogeneity of the sample, which is composed of a bulk region with relatively high conductivity and one or several relatively insulating thin layers. The equivalent circuit describing such a sample leads to a relaxation-like frequency and temperature dependence (10). The insulating layers can arise, for example, from surface effects (e.g., depletion regions of Schottky diodes at the electrodes) or internal barriers (e.g., grain boundaries). However, this is rather irrelevant from an application point of view (e.g., external surface layers are used to enhance the capacitance in ferroelectrics-based multi-layer ceramic capacitors). Thus, although in CCTO the exact mechanism is not yet finally clarified, the interest in this material is still high. This is, amongst others, demonstrated by the fact that since its discovery in 2000, twelve socalled "highly-cited" papers on this topic have appeared (source: ISI Web of Science, Nov. 2008). Unfortunately, at room temperature the relaxation in CCTO leads to a decrease of ε' in the MHz region and around GHz only values of the order of 100 are observed (8,11,12). In contrast, electron...