The ability of physics to provide an understanding of our Universe lies in the essential interrelation between experiment and theory. But physics does not provide us only reliable representations of the causes acting in nature. Its powerful experimental devices and theoretical methods are the underlying reason of the explosive technological development of our time. LiNbO3 and LiTaO3 represent only one example of the essential impact of both experimental and theoretical investigations on their technological applications. Particularly, LiNbO3 has been the subject of many experimental studies due to its applications in electro-optic and integrated optical devices. Also, the doped LiNbO3 with rare-earth and transition metals could be used, for instance, as a material for tunable lasers. The previous theoretical studies devoted to LiNbO3 and LiTaO3 focused on their electronic structure, being an attempt to understand the microscopic origin of the paraelectric-to-ferroelectric phase transition of these materials. The ab initio lattice dynamics investigations performed so far were mainly aimed to identify the role of the individual atoms vibrations in the energetic of the phase transition. The lack of a reliable model for the zone-center lattice dynamics in these compounds motivated us to investigate this issue by means of ab initio frozen-phonon calculations. On the background of the obtained phonon frequencies and eigenvectors, we unambiguously identified all zone-center modes for LiNbO3 and the A1 ones for LiTaO3. Due to the above mentioned enlargement of the technological applications of LiNbO3 by doping with various ions, we focused on the analysis of the ground-state properties of this material when doped with Fe and Cr. Even if the theoretical approach used in our calculations is not predictive with respect to the optical properties of the physical systems in study, a certain insight on this problem could be gained from the analysis of the effect of the atomic positions relaxation on the impurities energy levels localized in the optical band gap.