Because of steady increase in the availability of computing power, ab initio methods of computational materials science become everyday investigation tools in various research fields. This popularity of the first-principle-based atomistic modeling is in large part due to the performance of density functional theory (DFT), which could be used for simulations of chemically and structurally complex materials, including minerals, fluids and melts. However, because of intrinsic approximations, DFT is not always able to deliver reliable predictions. This is especially pronounced for f-elements bearing materials such as nuclear materials considered in nuclear waste management. Properties such as reaction enthalpies or electronic state are often badly predicted. In this contribution we discuss our experience with different computational methods, including the parameter free DFT+U method, in which the Hubbard U parameter is derived ab initio, for prediction of various properties of f electrons bearing materials. We show significant improvement obtained for structural and thermochemical parameters of various lanthanide-bearing ceramic materials and actinide-bearing molecular and solid compounds when the f electrons correlations are explicitly accounted for. Last, but not least, we demonstrate that complementary experimental and atomistic modeling studies result in superior and more complete characterization of challenging materials considered in nuclear waste management.