With the development of clean energy sources such as nuclear power, it has become more important to use advanced nuclear fuels to improve economic efficiency and expand safety margins. Thanks to the high fissile density, high thermal conductivity, and high melting point, uranium nitride and uranium silicide have been considered accident tolerant or high-performance fuels for commercial light water reactors and for future generation reactor systems. The composite fuel UO2-UN combining the high thermal conductivity and higher fissile density of UN and the excellent oxidation resistance of UO2 is also of interest. Great efforts have to be made to develop the fabrication of the advanced fuels and to qualify their performance. In this thesis, ab initio modeling is performed to contribute to this effort. Density functional theory is the basis for computing the electronic structure of materials in question, and a Hubbard correction term is added to handle the strongly correlated of electron interactions. The first part is focused on calculating or choosing suitable correction parameters, and the effect of the magnetic state of the investigated system is revealed. The second part is focused on the defect properties, including thermodynamics and kinetics. The latter is done by combining the DFT+U calculations with self-consistent mean-field theory. In addition, the stability of multi-phase systems are analyzed based on the defect properties and thermodynamics. Significant connection to experiments is made here. In the third part, the fracture properties of UO2 is modeled using an excess-energy assessment method, where the stress response of the grain boundaries and lattice UO2 is obtained. The impact of the fission products Xe and Mo on the fracture behaviors of both grain boundaries and lattices is discussed.