Within the framework of density functional theory, we have studied the electronic ground-state properties and approximated the optical dielectric constants and reflectivity of PbWO4 as well as CaWO4 and CdWO4. The band structure also provides insight int o the transport properties of excitons, electrons, and holes in these materials. A supercell adaptation of our calculation method which was previously applied to CaWO4:Pb at 50% concentration has now been used to study Pb vacancies, Bi impurities, and La impurities in PbWO4. Preliminary results of electronic structure calculations for CdWO4, having the wolframite structure, are presented for comparison.