Varistors are polycrystalline semiconductor devices with a highly nonlinear current-voltage characteristic. The non-linearity is caused by trapped electrons at the grain boundaries. The trapped electrons form an electric potential barrier, which is responsible for the high resistance at low voltages. The excess of a certain voltage, the breakdown voltage, leads to a decrease of the barrier by recombination of the trapped electrons with holes, generated by impact ionization. This decrease of the barrier results in an avalanche effect and in a drastic increase of the current within a small voltage range. Technical applications of varistors are, for example, overvoltage protection elements for electrical and electronic systems, by connecting in parallel with the protective circuit. The aim of the work is to analyze and describe relationships between the microstructural properties and the macroscopic current-voltage characteristics. For this purpose, a three-dimensional electrical varistor model was developed (network model), which is based on a realistic microstructure. With this network model the influence of microscopic grain boundary characteristic parameters on the electrical behavior of the components was investigated. Experimental investigations on different length scales revealed, that varistors can show a pronounced asymmetric behavior of the current-voltage-characteristic with respect to the voltage polarity. Pressure-dependent measurements of the current-voltage characteristic confirm a strong influence of mechanical stresses on the electrical conductivity. In addition, the mechanical stress enhance existing asymmetry of the characteristic. With the conventional varistor grain boundary model, these findings can not be described. In this work the barrier model has been extended by the effect of piezoelectric induced surface charges. This modified model has been used as input parameters for the network simulation of components. The modified model is the basis for the grain boundary characteristic, used in the network simulation of varistor components. All parameters of the simulations are based on realistic values. A simulation of the pressure-dependent measurements shows that the effects of mechanical stress on the electrical conductivity of components and the asymmetric behavior is described by the new model.