In this work, several lithium phosphate and thiophosphate materials are modeled to determine their optimized lattice structures, their total energies, and their electronic structures. Included in this study are materials characterized by isolated phosphate and thiophosphate groups – Li3PS4 and Li3PO4 and materials characterized by phosphate and thiophosphate dimers – Li4P2S6 and Li4P2O6 and Li4P2S7 and Li4P2O7. In addition, the superionic conducting material Li7P3S11 is also modeled as are recently discovered crystalline argyrodite materials Li7PS6 and Li6PS5Cl. A comparison of Li ion vacancy migration in Li4P2S7 and Li4P2O7 shows the migration energy barriers in the thiophosphate to be smaller (less than one-half) than in the phosphate.