A comparative first-principles study of the structural and optical properties of the alkali metal azides has been performed with density functional theory within the generalized gradient approximation. The crystal structures of the alkali azides compare well with experimental data. Their ionic character is manifested by the closeness of their internitrogen distances to the calculated N-N bond length for the free azide ion. An analysis of electronic structure, charge transfer, and bond order shows that the alkali azides are all wide-gap insulators and ionic compounds. The energy band and density of states for lithium azide and R-sodium azide are very similar, while these for potassium azide, R-rubidium azide, and R-cesium azide are alike, but some modifications are observed with the increment of alkali metals' electropositivity. These changes are closely related to the differences of the crystal structures. The general shapes of the real and imaginary parts of the dielectric function, adsorption coefficient, and electron energy-loss spectra are quite similar. The peaks originate from the electron transitions from the alkali metal s and p states to the conduction band. Our calculated optical properties for the alkali azides are found to be in good agreement with available experimental data. The absorption spectra of the alkali azides show a number of absorption peaks, which are believed to be associated with different exciton states, in the fundamental absorption region. In general, the electron energy-loss spectra have two plasma frequencies.