In perovskite oxides, layered perovskites and other complex-structured oxide families, a wide variety of distorted equilibrium structures and associated functional behavior can be realized, including ferroelectric, antiferroelectric, antiferrodistortive, and mixed-character structures. These structures can be understood as being produced by the freezing-in of one or more lattice instabilities of an appropriate high-symmetry reference structure. In this talk, I discuss how the information from first-principles studies of these systems provides guidance for altering the balance of the competition of instabilities of different character under conditions characteristic of epitaxial thin films, superlattices, and nanoparticles, leading to the realization of novel phases with structure and properties different from those of the bulk equilibrium phase. New ferroelectrics thus obtained could have combinations of tunable properties, including switchable polarization, magnetic ordering, and dielectric and piezoelectric response, desirable for current and future technological applications.