It is generally recognized that the formation of the fold-and-thrust tectonic structures of mobile belts on continents is associated with crushing and narrowing of the Earth’s crust as a result of collision of lithospheric plates. The deformation of the Caucasian lithosphere in the neotectonic time is generally consistent with these ideas. However, the block differentiation of the Caucasian lithosphere introduces specific features in the directivity of modern vertical and horizontal movements. In this paper, we analyze vertical movements of the Caucasus estimated by means of high-precision leveling over more than a century and consider their spatial correlation with tectonics, seismicity, stress-strain state, and geophysical fields. A clear relationship indicating the deep tectonic nature of the long-term uplifting of the Caucasus crust is revealed. Due to the differentiation of the Arabian plate movement, the territory of the Caucasus is divided into provinces that differ from each other in the pattern of modern movements, in the orientation of faults, and in the stress-strain state. The seismic regime in these provinces also has differences in the number of seismic events and focal mechanisms of the earthquakes. We propose a model of the deformation mechanism of the Greater Caucasus, which takes into account the long-term trend of the Caucasus uplifting in the conditions of general shortening of the Earth’s crust. The results of the analysis are used as a basis for discussion of a probable mechanism of tectonic evolution of the Greater Caucasus in the neotectonic time, which can be used in the assessment of seismic hazard in the North Caucasus.