LixFePO4 orthophosphates and fluorite- and pyrochlore-type zirconate materials are widely considered as functional compounds in energy storage devices, either as electrode or solid state electrolyte. These ceramic materials show enhanced cation exchange and anion conductivity properties that makes them attractive for various energy applications. In this contribution we discuss thermodynamic properties of LixFePO4 and yttria-stabilized zirconia compounds, including formation enthalpies, stability, and solubility limits. We found that at ambient conditions LixFePO4 has a large miscibility gap, which is consistent with existing experimental evidence. We show that cubic zirconia becomes stabilized with Y content of ~8%, which is in line with experimental observations. The computed activation energy of 0.92eV and ionic conductivity for oxygen diffusion in yttria-stabilized zirconia are also in line with the measured data, which shows that atomistic modeling can be applied for accurate prediction of key materials properties. We discuss these results with the existing simulation-based data on these materials produced by our group over the last decade. Last, but not least, we discuss similarities of the considered compounds in considering them as materials for energy storage and radiation damage resistant matrices for immobilization of radionuclides.