A theory is presented which quantitatively accounts for the important features of conduction in ZnO-based metal-oxide varistors. This theory has no adjustable parameters. Using the known values of the ZnO band gap, donor concentration n0, and low-voltage varistor leakage-current activation energy, we predict a varistor breakdown voltage of ?3.2 V/grain boundary for n0=1017 carriers cm−3 and T=300 °K. This compares well with measurements on a single grain-grain junction. The highly nonlinear varistor conduction derives from electron tunneling ’’triggered’’ by hole creation in the ZnO when the conduction band in the grain interior drops below the top of the valence band at the grain interface. The theory predicts coefficients of nonlinearity α=d (lnI)/d (lnV) as high as 50, or even 100.