The theory of ZnO varistors has evolved along with the increasingly detailed experimental description [1-2]. The extreme nonlinearity in the currentvoltage curves naturally led the early investigators to suggest the well-known nonlinear mechanisms, such as space-charge limited currents or electron tunneling. Later experiments made these first proposals untenable [3-9]. Recently a second generation of theories has been proposed, with many different mechanisms suggested for the extreme nonlinearity [10-15]. Here we wish to review these different theories, and also the experiments which bear upon their validity.