Key results of numerical geodynamic modeling of the structures of the lithosphere at the Institute of Physics of the Earth of the Russian Academy of Sciences are presented. Even in the very first models, the aim of these studies was to describe the time evolution of the boundaries of the layers composing the geological structures which is required for correlating the modeling results to the geological and geophysical data. In 1983, the equation of motion for the upper boundary of the model was complemented by the allowance of sedimentation and erosion. This equation provided the basis for building the geodynamic models of the formation of various types of sedimentary basins and made it possible to mathematically analyze the problem of estimating the rates of paleotectonic movements from thickness, age, and facies composition of sedimentary layers.
 New data on the formation and evolution processes of large-scale tectonic structures are obtained in the model of a rheologically stratified Earth’s boundary layer, asymptotically linked to mantle convection model. In particular, the role of the small-scale convection in the formation of lithospheric structures in the tectonic settings of extension and compression has been explored. The numerical results clearly demonstrate the key role of the small-scale asthenospheric convection in sedimentary basin formation (post-rift, on passive continental margins, in foredeep basins). The constructed models served as the basis for interpretation of heterogeneous geological and geophysical data in the context of geodynamic models. The examples of statement of inverse problems are presented and the relevant bibliography is provided.