It has been shown how the box discretization method can be applied to the drift-diffusion model and how the Scharfetter-Gummel method is used for current discretization. This is an established method used in most TCAD simulation environments [120,194,265]. A major part of this chapter is focused on vector discretization and three different approaches have been presented and analyzed. Finally, the topic of possible numerical problems in device simulation has been shortly discussed.