  The study of complex oxides and oxide heterostructures have dominated the
field of experimental and theoretical condensed matter research for the better
part of the last few decades. Powerful experimental techniques like molecular
beam epitaxy and pulsed laser deposition have made fabrication of oxide
heterostructures with atomically sharp interfaces possible, while more and more
sophisticated handling of exchange and correlations within first principles
methods including density functional theory (DFT) supplemented with Hubbard U
corrections and hybrid functionals, and beyond DFT techniques like dynamical
mean field theory (DMFT) have made understanding of such correlated oxides and
oxide interfaces easier. The emergence of the high mobility two dimensional
electron gas with fascinating properties like giant photoconductance, large
negative magnetoresistance, superconductivity, ferromagnetism, and the
mysterious coexistence of the latter two have indeed caught the attention of
condensed matter community at large. Similarly strain tuning of oxides have
generated considerable interest particularly after the recent discovery of
piezoelectric methods of strain generation. Theoretical understanding and
prediction of the possible exotic phases emerging in such complex oxides both
under strain and in heterostructures will eventually lead to better design of
device applications in this new emerging field of oxide electronics, along with
possible discovery of exotic physics in condensed matter systems which may be
of wider significance! In this review we briefly look at theoretical studies of
novel phenomena in oxides under strain and oxide heterostructures, and try to
understand the role of exchange and particularly correlation in giving rise to
such exotic electronic states.
