A general route to adjust the electrical performance of polymeric materials represents the composite approach, when fillers of different morphologies, sizes and electrical properties are embedded into a polymer matrix. The resulting macroscopic properties of the composite material depend on the volume fraction and the spatial distribution of the fillers as well as on their interaction with the polymeric material. The current contribution aims to develop a complete theoretical description of the electrical and dielectric properties of multiphase composite materials in systematic dependence on morphology, volume fraction, form factor, orientation, presence interphases and gradients of local properties. Three scientific challenges are addressed: (a) Understanding the impact of internal interfaces and interphases on the dielectric response of composite materials; (b) Detailed quantitative analysis of the impact of heterogeneity on the spectral dependence of existing molecular relaxation processes; (c) To develop and propose a criterion which enables one to distinguish, in the case heterogeneous materials, true relaxation processes from dielectric dispersions caused by the phenomenon of interfacial polarization.