  Oxide heterostructures are a new class of materials by design, that open the
possibility for engineering challenging electronic properties, in particular
correlation effects beyond an effective single-particle description. This short
review tries to highlight some of the demanding aspects and questions,
motivated by the goal to describe the encountered physics from first
principles. The state-of-the-art methodology to approach realistic many-body
effects in strongly correlated oxides, the combination of density functional
theory with dynamical mean-field theory, will be briefly introduced. Discussed
examples deal with prominent Mott-band- and band-band-insulating type of oxide
heterostructures, where different electronic characteristics may be stabilized
within a single architectured oxide material.
