A comprehensive theory of conduction in polycrystalline silicon is presented. The present approach fundamentally differs from previous theories in its treatment of the grain boundary. This theory regards the grain boundary as an amorphous conducting medium and invokes drift-diffusion as the mechanism of conduction. This model explains the electrical properties of polysilicon in terms of the inherent electronic and structural parameters of the material and is in excellent agreement with the experimental data. The theory is valid for arbitrary grain size, temperature, doping concentration, and applied voltage. Therefore, this model is suitable for describing electrical characteristics of laser restructured and/or plasma passivated polysilicon and of devices fabricated therein. Also, the present approach critically examines, theoretically and experimentally, the grain boundary scattering potential, qx, introduced in previous theories. Specifically, the emission mode of conduction based on qx is shown to suffer from the inconsistencies in its voltage partition scheme and theoretical I-V predictions. The present model consistently incorporates the effect of mobile carrier redistribution under bias and accounts for the high field switching in amorphous grain boundary. Microscopic mobilities used for describing the carrier transport provides a physical basis for introducing the grain voltage (V(,a)) across the unit cell of polysilicon system and V(,a), in turn, distributes itself to preserve a constant current density therein. This new criterion yields a new voltage partitioning scheme, and a general expression for corresponding response function of current is derived in terms of pertinent system parameters.