In recent years, there has been an increasing demand for materials that can serve for a variety of technological applications, such as nonvolatile ferroelectric random access memory for computers, SONAR sensor device for military vehicles, dielectric materials for telecommunication, and photovoltaic materials for solar energy conversion. In this thesis, we present computational studies of a special class of complex oxides. Specifically, we studied perovskite ferroelectric materials with the general chemical formula ABO3, where A and B correspond to different chemical species. Using computational and theoretical tools, we started our search for novel materials by improving our understanding of how the microscopic chemistry and physics determine the macroscopic properties of materials that have been previously synthesized and characterized. Thus, having validated our computational methods, we used those to predict novel materials with superior properties and further developed some general rules and guidelines for the design of novel materials. Depending on the specific problem at hand, we used either ab initio density functional theory (DFT) or classical molecular dynamics (MD) modeling. First, we employed ab initio DFT to investigate the material Bi(Zn1/2Ti1/2)O3 (BZT), which is considered to be good analogue of the more commonly used PbTiO3. Although PbTiO3 is ubiquitously used, a lead free ceramics, such as Bi(Zn1/2Ti1/2)O3, is desirable due to environmental concerns. Our results confirm the material's superior large cation displacement and tetragonal distortion compared to PbTiO3, but also indicate that the conventional electrostatic model (for determining the most favored cation ordering) should be corrected under special lattice geometric circumstances. As the tetragonal distortion increases, the electrostatic contribution to the total energy decreases, rendering other interaction forces relatively more important in determining the ordering of cations. Inspired by our work on BZT, we continued to develop a guideline for designing ferroelectric materials with similar lattice parameters (high tetragonality). Traditionally, Landau-Ginzburg-Devonshire (LGD) theory has been considered a powerful tool for studying ferroelectrics, which relies on the polarization (P) as the order parameter. However, the lack of LGD parameters limits the utility of LGD theory when applied to novel materials with compositional variation, requiring the development of an alternative design rule. To this end, we began by carefully choosing a group of PbTiO3-derived solid solutions. By extracting the essential geometric information (ionic displacement and strain) as well as the polarization of the solutions, we discovered a very good linear correlation between B-cation displacement squared and strain for all 25 solid solutions, suggesting that the B-cation displacement is a more natural order parameter rather than the polarization of the material. Furthermore, we found that the magnitude of the ionic displacement is mostly affected by both the ion covalency and the ion sizes, allowing us to increase the B-cation displacement by substituting the B-site with either a small-size cation or the small fraction of a large-size cation surrounded by rigid TiO6 neighbors. The advances we made in this work contribute a significant piece to the big picture of understanding the relationships between different microscopic and macroscopic properties for perovskite ferroelectrics. Next, we turned our attention to the electronic structures for those highly tetragonal ferroelectric materials that we studied so far only the structural properties. We chose three target materials, namely Bi(Zn1/2Ti1/2)O3, Bi(Zn3/4W1/4)O3 and Bi(Zn3/4Mo1/4)O3. All of these materials have two types of B-cations. Different local chemistries, including B-cation ordering, lattice strain, cation identity and oxygen cage O6 tilt, affect the electronic band gap structure. We found that the cation ordering effect most profoundly affects electronic band gaps in these materials, which also changes the carrier mobility accordingly. More importantly, we discovered that by reorienting the polarization direction by 90o, the band gap can be altered by as much as 0.6 eV. This result highlights the possibility of using a single chemical composition compound for multi-junction solar energy conversion. By arranging cations differently at different layers, different layers would absorb different frequencies of photons of the solar spectrum. Finally, we utilized a classical bond-valence model (BVMD) to trace the ferroelectric material's fast dynamics under external perturbations, such as electric field or strain field. One of our studies is about the polarization switching dynamics of the prototypical perovskite ferroelectric PbTiO3, by coherently controlling the collective structural change. A specially shaped terahertz electric field pulse train is pumped to resonate with a particular IR-active phonon mode. We proved that the atoms in the crystal could move collectively from the initial domain orientation to the opposite one during a very short time period (15 ps), suggesting a new time scale for ultrafast read'' and write'' speed in computers equipped with ferroelectric non-volatile random access memory. Also, we employed MD simulations to study the domain wall nucleation dynamics under an external strain field. The 90o domain wall width is observed to be around one or two lattice constants thick, consistent with other DFT studies, high-resolution transmission electron microscopy (HRTEM), and atomic force microscopy (AFM) experiments. A very interesting antisymmetry at the wall was revealed with atomic scale details. Our preliminary data for the domain wall nucleation process shows a good match with Merz's law. Additional 90o domain wall nucleation under strain dynamics studies are currently under investigation.