Localized impurities doped in the semiconductor substrate of nanostructure devices play an essential role in understanding and resolving transport and variability issues in device characteristics. Modeling discrete impurities under the framework of device simulations is, therefore, an urgent need for reliable prediction of device performance via device simulations. In the present paper, we discuss the details of the physics associated with localized impurities in nanostructure devices, which are inherent, yet nontrivial, to any device simulation schemes: The physical interpretation and the role of electrostatic Coulomb potential in device simulations are clarified. We then show that a naive introduction of localized impurities into the Poisson equation leads to a logical inconsistency within the framework of the drift-diffusion simulations. We describe a systematic methodology for how to treat the Coulomb potential consistently with both the Poisson and current-continuity (transport) equations. The methodology is extended to the case of nanostructure devices so that the effects of the interface between different materials are taken into account.