Energy needs are projected to continue to increase in the coming decades, and with the drive to use more clean energy to combat climate change, nuclear energy is poised to become an important player in the energy portfolio of the world. Due to the unique nature of nuclear energy, it is always vital to have safe and efficient generation of that energy. In current light water reactors, the most common fuel is uranium dioxide (UO2), an oxide ceramic. There is also ongoing research examining uranium-based based metallic fuels, such as uranium-molybdenum (U-Mo) fuels with low uranium (U) enrichment for research reactors as part of a broader effort to combat nuclear proliferation, and uranium-zirconium-based fuels for Generation IV fast reactors. Each nuclear fuel has weaknesses that need to be addressed for safer and more efficient use. Two major challenges of using UO¬2 are the fission gas (e.g. xenon) release and the decreasing thermal conductivity with increasing burnup. In UMo alloys, the major weakness is the breakaway swelling that occurs at high fission densities. The challenges presented by both fuel types are heavily impacted by microstructure, and several studies have identified that the initial microstructure of the fuel in particular (e.g. initial grain size and grain aspect ratio) plays a large role in determining when and how quickly these processes occur. Thus, knowledge of how such initial microstructures evolve is paramount in having stable and predictable fission gas release and thermal conductivity decrease (in UO2) and fuel swelling (in UMo alloys). Mobility is a critical grain boundary (GB) property that impacts microstructural evolution. Existing literature examines GB mobility for a few specific boundaries but does not (in general) identify the anisotropy relationships that this property has. This work first examined the anisotropy in GB mobility, specifically identifying the anisotropy trend for the low-index rotation axes for tilt GBs in BCC γ U, and fluorite UO2 via molecular dynamics simulation. GB mobility is calculated using the shrinking cylindrical grain method, which uses the capillary effect induced by the GB curvature to drive grain growth. The mobilities are calculated for different rotation axes, misorientation angles, and temperatures in these systems. The results indicated that the density of the atomic plane perpendicular to the (tilt) GB plane (which is also perpendicular to the rotation axis) significantly impacts which GB rotation axis has the fastest boundaries. Specifically, the atomic plane that has a higher density tends to have a faster mobility, because it is more efficient for atoms moving across the GB along such planes. For example, for body-centered cubic materials, the <110> tilt GBs are determined to have the fastest mobilities, while face-centered cubic (FCC) and FCC-like structures such as fluorite have <111> tilt GBs as the fastest. Knowledge of GB mobility and its anisotropy in pure materials is helpful as a baseline, but real materials have solutes or impurities (both intentionally and unintentionally) which are known to affect GB mobility by processes such as solute drag and Zener pinning. Additionally, in reactors, nuclear fission can produce many fission products, each of which acts as an additional impurity that will interact with the GB in some way. Because the initial microstructure and its subsequent evolution are vital for addressing the challenges of using nuclear fuel as described above, knowledge of the impacts of these impurities on GB mobility is required. Therefore, this work examined the impact of solutes and impurities on GB mobility and its anisotropy. In particular, the solute effect was examined using the UMo alloy system, while the impurity effect was examined using Xe (a very common fission product) in the γ U, UMo, and UO2 systems. It is found that both Mo and Xe can cause a solute drag effect on GB mobility in the γ U system, with the effect of Xe being stronger than Mo at the same solute/impurity concentration. Xe also causes a solute drag effect in UO2, though the magnitude of the effect is interatomic-potential-dependent. The mobility anisotropy trend was found to disappear at high solute and impurity concentrations in the metallic U and UMo systems but was largely unaffected in the UO2 system. These results not only increase our fundamental understanding of GB mobility, its anisotropy, and solute/impurity drag effects, but also can be used as inputs for mesoscale simulations to examine polycrystalline grain growth with anisotropic GB mobility and in turn examine how the fuel performance parameters change with these properties. / Doctor of Philosophy / Worldwide, energy needs continue to increase each year. Concerns related to climate change have led to an increased emphasis on renewable energies such as solar and wind, but the limitations of these resources prevent them from being the only energy sources. Nuclear energy is uniquely positioned to address several energy concerns: it is clean (no carbon emissions and air pollution), reliable (for example, 24/7 energy production, independent of weather), and energy-dense (one kilogram of fissile uranium provides roughly the same amount of energy as 3000 metric tons of coal). Currently, nuclear energy provides roughly 20% of the energy of the United States, but future predictions show a decrease in the total share of energy generation due to aging systems and a limited number of new reactors being built. The safety and efficacy of existing and future reactors are among the primary concerns for being able to allow nuclear energy to increase its energy share. To determine the safety and efficacy of new reactor designs, a computer simulation tool called fuel performance modeling has been used over the last few decades. This tool requires several material properties as input, one of which is how the nuclear reactor fuel microstructure changes based on a variety of conditions. A significant process contributing to microstructural change is grain growth. Grains (crystallites that make up the whole material) meet at interfaces called grain boundaries (GBs), and these GBs have two properties that largely determine how grain growth occurs: energy and mobility. Significant effort is being put into understanding these properties and their anisotropy, or how they change based on the GB character which is the relative mismatch between the two grains. This work contributes additional understanding of GB mobility anisotropy in two nuclear fuels: uranium dioxide (UO2, the primary fuel in current reactors) and a uranium-molybdenum (UMo) alloy (the primary fuel for newer research reactors). In particular, computer simulation is used to determine GB mobility for several unique GB systems. It is found that for pure nuclear fuels, GB mobility anisotropy is largely determined by which atomic plane has the highest density perpendicular to the GB. When the fuel is no longer pure (through the addition of alloying elements or other impurities) the anisotropy changes significantly in UMo fuels, such that at high concentrations of solute or impurities there is little to no anisotropy, while very little change is observed in the anisotropy in UO2.