Complex oxides exhibiting a wide variety of novel functional properties such as ferromagnetism and ferroelectricity have been extensively studied during the past decades. Recent advances in the field of oxide heteroepitaxy have made it possible to create and control hybrid oxide heterostructures with abrupt epitaxial interfaces. The oxide heteroepitaxy with the capability of controlling interface composition, strain, length scales, etc. has opened the totally new and exciting scientific avenue and has offered potential device applications to be explored. Epitaxial integration of functional oxides on semiconductor such as Si (001) and Ge(001) is of great interest, as it potentially leads to further technological development of these interesting oxide systems. In this dissertation, using density functional theory we explore physics and chemistry of novel oxide heterostructures and issues related to the integration of functional oxides on semiconductors. Oxide materials that are studied in this dissertation include polar LaAlO₃, high-k dielectric SrTiO₃, photocatalytic anatase TiO₂ and CoO, and strongly correlated magnetic oxide LaCoO₃. / text