Uranium and lithium oxides are superionic conductors whose solid-state diffusion coefficients are comparable to that of liquids. They are also of technological importance to the nuclear industry. A detailed study of their physical and thermodynamic properties is of great interest for enhanced understanding of these systems. We review our lattice dynamics and molecular dynamics studies carried out on UO2 and Li2O in their normal as well as superionic phase. Lattice dynamic calculations have been carried out using shell model in the quasiharmonic approximation. The calculated elastic constants, phonon frequencies and specific heat are in good agreement with the reported experimental data. Lattice dynamics calculations of the thermodynamic properties help validate the interatomic potentials required for undertaking molecular dynamics simulations to study the diffusion behavior in UO2 and Li2O. The diffusion constant of Li in Li2O and O in UO2 have been determined and compared with the experiment. The calculated superionic transition temperature of Li2O is 1000 K while that of UO2 is 2300 K. With the help of molecular dynamics simulations the microscopic picture of the local structure of the lattice just beyond the transition temperature has been deduced. The structural behavior of UO2 and Li2O, have also been simulated at high pressure. UO2 is found to undergo a sluggish transformation to a high-pressure cotunnite phase at about 40 GPa. Similarly Li2O reveals an anti-fluorite to anti-cotunnite transformation (as reported in angle dispersive X-ray studies) at about 50 GPa. Our lattice dynamical calculations show up similar transformations for UO2 and Li2O at 70 and 25 GPa respectively.