Theory-based models and high performance simulations are briefly reviewed starting with atomistic methods, such as Electronic Structure calculations, Molecular Dynamics, and Monte Carlo, continuing with meso-scale methods, such as Dislocation Dynamics and Phase Field, and ending with continuum methods that include Finite Element and Finite Volume. Special attention is paid to relating thermo-mechanical and chemical properties of the fuel to reactor parameters. By inserting atomistic models of point defects into continuum thermo-chemical calculations, a model of oxygen diffusivity in $UO_{2+x}$ is developed and used to predict point defect concentrations, oxygen diffusivity, and fuel stoichiometry at various temperatures and oxygen pressures. The simulations of coupled heat transfer and species diffusion demonstrate that including the dependence of thermal conductivity and density on composition can lead to changes in the calculated centerline temperature and thermal expansion displacements that exceed 5%. A review of advanced nuclear fuel performance codes reveals that the many codes are too dedicated to specific fuel forms and make excessive use of empirical correlations in describing properties of materials. The paper ends with a review of international collaborations and a list of lessons learned that includes the importance of education in creating a large pool of experts to cover all necessary theoretical, experimental, and computational tasks.