This thesis provides a simple model to describe the highly nonlinear electrical behaviour of zinc oxide varistors. It is well known that the current through varistors is determined by so-called double Schottky barriers at the zinc oxide grain boundaries. The presented approach of this work is novel insofar as the grain boundary characteristics, which are part of every varistor model, are based on experimental data, namely micro 4-point probe measurements. Furthermore, it is the first model where also the electrode-ceramic interface (electrode-to-grain junctions) is incorporated. Another point on which a lot of emphasis is placed is asymmetric current-voltage (I-V) behaviour of the grain boundaries, which is not well discussed in the literature. The measurements showed that most grain boundaries have an asymmetric characteristic, i.e. the forward and reverse I-V curves do not overlap. A theoretical attempt to explain this asymmetry is able to provide arguments why such asymmetry is possible, although the experimental data could not be fully explained. With regard to varistor modelling, a completely new approach could be found. It is shown that the current through the zinc oxide microstructure - with thousands of grain boundaries - behaves equivalent to the sum of the current of paths with different numbers of grain boundaries connected in series. To the authors' knowledge, this is the first model that describes the I-V behaviour and explains the gradual increase in current through low-voltage varistors.