We present theoretical studies of electronic structures, optical responses, and phonon modes of undoped HgI2 in its red tetragonal form. The electronic band structure is studied via an empirical nonlocal pseudopotential model, including the spin-orbit interaction. The electron and hole effective masses, optical matrix elements for interband transitions, and complex dielectric function are computed. Excitonic effects on the absorption coefficient near the fundamental band gap are included within the effectivemass approximation. The resulting absorption spectra and their polarization dependence are compared with experiment with favorable agreement. The phonon modes of HgI2 are studied with a microscopic model and a good fit to the neutron scattering data is obtained.