The increasing demand for realizing ultra-fast, compact, and ultra-low power electronics/spintronics has propelled the creation of novel multiferroic heterostructures which enable voltage control of magnetism in an energy efficient way. In this progress report, we present an overview of recent advances and future prospects of the most attractive oxide multiferroic heterostructures, with an emphasis on the development of strong magnetoelectric coupling effects and their device applications. In particular, we review the recent progress in spinel/ferroelectric and garnet/ferroelectric multiferroic oxide heterostructures.