A dielectric loss model based on the tunneling of electrons from metal electrodes into traps in the insulator near the interface is described. The temperature dependence of the losses is controlled primarily by the energy distribution of the traps and the frequency dependence is controlled by their spatial distribution. Traps distributed uniformly in both energy and space result in essentially temperature- and frequency-independent losses. The model predicts an inverse dependence of losses on sample thickness. The step-response currents for the tunnel mechanism become nonlinear at high applied fields; however, the detailed behavior is very sensitive to the trap distribution assumed. For a particular trap distribution it is possible to have a polarity-dependent, irreversible step response.