The properties of numerous technologically important materials are determined by the crystal structure. Understanding the relationship between a material's properties and its crystal structure allows materials with specific properties to be designed by modifying or controlling the crystal structure. Many materials have been designed using chemical intuition which is continually improved as more and more materials are made. This process relies on new materials being synthesized and characterized, which often requires significant time and effort. Density functional theory was developed more than half a century ago and provides a way to simulate the electronic structure, and therefore numerous properties of a crystal structure. Combined with ever improving computational abilities, in many cases it has become easier to study materials by simulating their properties than synthesizing them. While these simulations do not perfectly replicate the properties of a real material, the predictions of simulations are often reliable enough to serve as a guide for where to focus experimental efforts. Simulations provide a straightforward way to study crystals that may not be possible to synthesize experimentally because the crystal structure is completely controlled during a simulation, whereas the laws of physics control an actual crystal structure. This precise control over the crystal structure allows the relationship between crystal structure and a material's properties to be easily and directly probed. Once this relationship is understood, efforts can be made to force a material to form in a crystal structure with desirable properties. This dissertation presents several computational studies, primarily using density functional theory, of crystal structures and their relationship to macroscopic properties. La2SrCr2O7 was studied to explain why it forms in a never before seen crystal structure. A coupling between A-site disorder, B-site chemistry, and octahedral rotations was found and provides a route towards controlling the crystal structure in related materials. Antiferroelectricity was studied in PbZrO3 and found to be dependent on a flat energy landscape encompassing nonpolar and polar structures. Ideas for future work to improve the understanding of antiferroelectricity and possibly designing new antiferroelectrics are discussed. Finally, the crystal structure of Ln2NiO4+delta was studied, paying particular attention to the arrangement of excess oxygen atoms. These arrangements have a significant effect on the properties of Ln2NiO4+delta and should be considered in future computational studies.