The heart of materials science is understanding the relationship between structure (how molecules are connected at the atomic level, as well as in hierarchical building blocks) and properties. Historically this has been achieved by studying the properties of materials in hand, either found in nature or synthesized in the laboratory. As the understanding of the relationship between structure and properties has grown, and our ability to calculate and in particular to solve Schrödinger’s equation for solids has improved, so too has our desire and ability to predict structures with enhanced properties through computation. In this thesis I do each of those three tasks – prediction, synthesis, and characterization – on a system that is of interest in its own right and which I hope may yield results that can be applied to other materials systems as well. All of these systems are materials in the highly-versatile perovskite structure, which can accommodate most of the elements of the periodic table. Perovskites have been the object of much study in the laboratory as well as being used extensively in industrial applications, with such properties as ferroelectricity, piezoelectricity, ferromagnetism, and superconductivity. First, I delineate the chemical factors that determine the ground-state structure of CsPbF3. I use CsPbF3 as a guide to search for rules to rationally design from first principles new polar fluoride and halide perovskites with stoichiometry ABX3 and as a model compound to study the interactions of lone pair electrons, antipolar structural distortions, and the different coordination requirements of A and B cations. I show that the coordination requirements of the A-site cation Cs+ and the stereoactivity of the B-site lone pair cation Pb2+ compete or cooperate via the anionic displacements that accompany polar distortions, and consider the generalizability of my findings to other halide and oxide perovskites. Next, I describe the chemical reactions that govern growth of PbTiO3 and BiFeO3 by molecular-beam epitaxy. PbTiO3 and BiFeO3 are among two dozen complex oxides that are grown by MBE using thermodynamic composition control. I show that kinetics are also critical to growing phase-pure materials by this method, and that oxidation of lead or bismuth can be the rate-limiting step in the synthesis of PbTiO3 or BiFeO3, respectively, from component elements. I establish a simple kinetic model for the growth of these materials that complements the existing thermodynamic theories and delineate the factors controlling the range of temperatures and pressures in which kinetics permit these materials to be grown by thermodynamic control. Finally, I detail how to predict and verify the presence of hybrid reflections in x-ray diffraction patterns of phase-pure epitaxial oxide thin films grown on single-crystal substrates. I present symmetric θ-2θ scans of such films of PbTiO3, BaxSr1−xTiO3, and layered perovskite-relative La2NiO4, in which there occur peaks (reflections) that correspond to neither the film nor the substrate crystal structure, and argue that these peaks are the result of multiple diffraction from both the film and substrate. I describe a simple method to predict and identify peaks resulting from hybrid reflections.