Ab-initio calculations are an important tool for reliable predictions of structural and electronic properties of individual semiconductor heterojunctions, but are also essential for understanding the underlying mechanisms, establishing a rationale for the peculiarities of entire classes of heterojunc- tions, and gaining the necessary insight to engineer their properties for specific applications. In this Chapter, we present the basic ingredients of an ab-initio approach to the problem and discuss their application to prototypical systems. Among the electronic properties, particular emphasis is placed on the band offsets, which are the key parameters governing the transport properties of a junction, but other features are also discussed, such as localized electron states at interfaces and cross-sectional scanning tunneling microscopy images. We focus mostly on ab-initio computations and theoretical models derived from first–principle numerical experiments.
