The paper proposes an approach for describing the electrical characteristics of electrostatically precipitated dust layers. It describes the macroscopic electrical properties of the dust layer, by couplinag the current transport equation and Poisson's Equation. It attributes the electrical breakdown of the dust layer to enhanced values of the local electric field due to the combined effects of polarization in the dielectric layer and the contribution to the electric field from the space charge distribution in the layer. Models based on this approach appear to offer the potential for describing the observed electrical behavior. It also discusses the experimental data which are needed for developing this approach.