A new type of voltage dependent resistors (varistors), based on zinc oxide ceramics with several other metal oxides as additives, has recently been investigated. The microstructure of these varistors consists of ZnO grains surrounded by thin insulating metal oxide barriers. We present experimental evidence to show that the highly non-linear current-voltage characteristics, with α-values (α = dlogI/dlogV) in excess of approximately 60 at room-temperature, can be described by the properties of an isolated junction between two ZnO grains. Guided by these and other experimental observations, we discuss several simplified versions of a theoretical model based on the assumption of an nnn or npn junction with its associated depletion regions, surface states, donor and acceptor states. We find that none of these simplified models can lead to α ≳ 25 within a current and voltage range that is consistent with the experimental observations. Only an inclusion of tunneling out of the surface states can in principle lead to larger values of α. On the other hand, a simple space charge current based on trap states in the middle region is shown to give sufficiently high α-values when the injection problem at the space charge boundary is neglected. We conclude that a correct quantitative description of the varistor behaviour must involve a rather complex junction model which includes additional mechanisms, such as e.g. space charge effects or tunneling out of surface states.