Detailed ab initio studies on the electronic structure and optical properties of the heavy-metal azides have been performed using density functional theory within the generalized gradient approximation. An analysis of band structure, density of states, charge transfer, and bond order shows that the heavy-metal azides are ionic compounds but have covalent character. The valence bands of AgN3 and CuN3 are strongly dominated by Ag- and Cu-d, respectively, but that of TlN3 arises from the contributions of Tl-s and terminal N-p and not from Tl-d. The real and imaginary parts of the dielectric function, adsorption coefficient, and electron energy-loss spectra are calculated and compared with available experimental data.