Abstract Within the density functional theory framework, we investigate the structural, electronic, vibrational, dielectric, piezoelectric and optical properties of hexagonal lithium iodate, including some nonlinear response properties, like the nonlinear dielectric (electronic) susceptibility, the electro-optic tensor and the Raman tensor. Beyond the comparison with available experimental data and the associated analysis, we predict the values of several properties or characteristics of this material, e.g. the phonon frequencies with B symmetry, that are silent in both IR and Raman experiments, the Born effective charges, for which a detailed analysis is performed, Raman susceptibilities and the decomposition of the clamped electro-optic tensor in terms of the different modes. The agreement with available experimental results is reasonable to excellent, depending on the property. The lattice parameters and macroscopic dielectric constants agree to the experimental ones within 2%. The Kohn–Sham electronic bandstructure is predicted, but suffers from the well-known DFT band gap problem. Reflectivity spectra computed with the density functional perturbation theory are in qualitative and quantitative agreements with experiments for incident light along the two main hexagonal axes. The phonon frequencies at the Brillouin zone center are, in average, 5.74% apart from the experimental one. The previous assignment of Raman features is discussed, on the basis of our computed Raman spectra, including relative peak heights. Finally, this study confirms theoretically the large nonlinear coefficients d31 and d33 of −6.6pm/V and −7.5pm/V as well as its noteworthy piezoelectric and electro-optic properties that make this material remarkable.