Remarkable properties of relaxor ferroelectrics are related, first of all, to the complicated dipolar dynamics observed in these materials. Dynamical characteristics of relaxors and, in particular, the classical lead oxide perovskite relaxors have been studied in numerous works using different experimental techniques including dielectric spectroscopy, inelastic neutron, x-ray and light scattering, infrared spectroscopy, etc. Many unusual effects have been observed such as extremely large electric permittivity characterized by the diffuse maximum in the temperature dependence and dielectric relaxation arising from several polarization mechanisms, softening of several lattice vibration modes with temperature, mysterious “waterfall” effect associated with one of the modes, etc. However, none of the existing experimental techniques is able to explore the full desirable range of temperatures, energies, eigenvectors and amplitudes. Therefore, different dipolar excitations are often to be studied by different methods and both the relation between these excitations and their role in the formation of relaxor behaviour remain controversial. This is the primary reason why the basic mechanisms of relaxor ferroelectricity are still unknown. Here we report the first successful atomistic simulation of the dipolar dynamics in lead oxide perovskite relaxor crystal which reproduces quantitatively the known experimental results obtained by different methods. The first-principles-based molecular dynamics simulations applied to the prototypical relaxor PbMg1/3Nb2/3O3 allowed, in particular, to reveal the soft transverse optic phonon mode responsible for the ferroelectric phase transition, analyze the subterahertz relaxation dynamics and relate the empirically known characteristic temperatures to structural and dynamical features.