Being a part of ongoing continental collision between the Arabian and Eurasian plates, the Caucasus region is a remarkable site of moderate to strong seismicity, where devastating earthquakes caused significant losses of lives and livelihood. In this article, we survey geology and geodynamics of the Caucasus and its surroundings; magmatism and heat flow; active tectonics and tectonic stresses caused by the collision and shortening; gravity and density models; and overview recent geodetic studies related to regional movements. The tectonic development of the Caucasus region in the Mesozoic-Cenozoic times as well as the underlying dynamics controlling its development are complicated processes. It is clear that the collision is responsible for a topographic uplift / inversion and for the formation of the fold-and-thrust belts of the Greater and Lesser Caucasus. Tectonic deformations in the region is influenced by the wedge-shaped rigid Arabian block indenting into the relatively mobile region and producing near N-S compressional stress and seismicity in the Caucasus. Regional seismicity is analysed with an attention to sub-crustal seismicity under the northern foothills of the Greater Caucasus, which origin is unclearwhether the seismicity associated with a descending oceanic crust or thinned continental crust. Recent seismic tomography studies are in favour of the detachment of a lithospheric root beneath the Lesser and Greater Caucasus. The knowledge of geodynamics, seismicity, and stress regime in the Caucasus region assists in an assessment of seismic hazard and risk. We look finally at existing gaps in the current knowledge and identify the problems, which may improve our understanding of the regional evolution, active tectonics, geodynamics, shallow and deeper seismicity, and surface manifestations of the lithosphere dynamics. Among the gaps are those related to uncertainties in regional geodynamic and tectonic evolution (e.g., continental collision and associated shortening and exhumation, lithosphere structure, deformation and strain-stress partitioning) and to the lack of comprehensive datasets (e.g., regional seismic catalogues, seismic, gravity and geodetic surveys).

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Typically, strong earthquakes do not occur over the entire territory of the seismically active region. Recognition of areas where they may occur is a critical step in seismic hazard assessment studies. For half a century, the Earthquake-Prone Areas (EPA) approach, developed by the famous Soviet academicians I.M. Gelfand and V.I. Keilis-Borok, was used to recognize areas prone to strong earthquakes. For the modern development of ideas that form the basis of the EPA method, new mathematical methods of pattern recognition are proposed. They were developed by the authors to overcome the difficulties that arise today when using the EPA approach in its classic version. So, firstly, a scheme for the recognition of high seismicity disjunctive nodes and the vicinities of axis intersections of the morphostructural lineaments was created with only one high seismicity learning class. Secondly, the system-analytical method FCAZ (Formalized Clustering and Zoning) has been developed. It uses the epicenters of fairly weak earthquakes as recognition objects. This makes it possible to develop the recognition result of areas prone to strong earthquakes after the appearance of epicenters of new weak earthquakes and, thereby, to repeatedly correct the results over time. It is shown that the creation of the FCAZ method for the first time made it possible to consider the classical problem of earthquake-prone areas recognition from the point of view of advanced systems analysis. The new mathematical recognition methods proposed in the article have made it possible to successfully identify earthquake-prone areas on the continents of North and South America, Eurasia, and in the subduction zones of the Pacific Rim.

The article presents the results of FCAZ-recognition of the strongest (≥ 7.75) earthquakeprone areas on the Pacific coast of the Kamchatka Peninsula and strong (≥ 6.5) earthquakeprone areas in California. For the first time, earthquake epicenters from declustered catalogs were used as recognition objects. Based on the example of the considered regions it is shown that the presence of foreshock and aftershock sequences in the earthquake catalogs does not significantly affect the results of FCAZ-recognition based on the clustering study of weak earthquake epicenters.

Strong earthquake-prone areas recognition (≥ 6.0) in the Caucasus is performed by means of the new "Barrier-3" pattern recognition algorithm. The obtained result is compared with potentially high seismicity zones recognized previously using the "Cora-3" pattern recognition algorithm. It is proposed to define an interpretation of the integral recognition result by the "Barrier-3" and "Cora-3" algorithms as a fuzzy set of recognition objects in the vicinity of which strong earthquakes may occur in the Caucasus.