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 bandband-insulating type of oxide heterostructures, where different electronic characteristics may be stabilized within a single architectured oxide material.