Oxides based on the perovskite crystal structure exhibit a rich variety of physical properties, in which virtually every known ground state can be found - insulator, semiconductor, metal, superconductor, heavy fermion, ferromagnet, antiferromagnet, spin glass, charge/spin density wave, ferroelectric, piezoelectric, etc. Many of these systems are lattice-matched within a few percent of one another, leading to the possibility of complex oxide heteroepitaxy. Our long-term goal is to develop this field and utilize the many degrees of freedom available, in an extended analogy to compound semiconductor heterostructures, which has historically emphasized the manipulation of single-particle charge states. Toward this end, we are growing oxide thin films using pulsed laser deposition, emphasizing precise growth with atomic precision. One recent focus has been the study of the charge structure at the interface between a Mott (correlation gap) insulator and a band (single-particle gap) insulator. Both in our own laboratory as well as through collaborations, we are investigating magnetotransport properties, optical response, and a variety of scanning probe spectroscopies. In this manner we are building the fundamental understanding required to engineer novel states in oxide heterostructures.