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Oxide heterostructures have been shown to exhibit unusual physics and hold the promise of novel electronic applications. We present a set of criteria to select and design interfaces, particularly those that can sustain a high-density two-dimensional electron gas (2DEG). We describe how first-principles calculations can contribute to a qualitative and quantitative understanding, illustrated with the key issue of band alignment. Band offsets determine on which side of the interface the 2DEG will reside, as well as the degree of confinement. We use hybrid density functional calculations to determine the band alignments of a number of complex oxides, considering materials with different types of conduction-band character, polar or nonpolar character and band insulators as well as Mott insulators. We suggest promising materials combinations that could lead to a 2DEG with optimized properties, such as high 2DEG …