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An active stage of relativistic astrophysics started in 1963 since in thisyear, quasars were discovered, Kerr solution has been found and the first TexasSymposium on Relativistic Astrophysics was organized in Dallas. Five yearslater, in 1967--1968 pulsars were discovered and their model as rotatingneutron stars has been proposed, meanwhile J. A. Wheeler claimed that Kerr andSchwarzschild vacuum solutions of Einstein equations provide an efficientapproach for astronomical objects with different masses. Wheeler suggested tocall these objects black holes. Neutron stars were observed in differentspectral band of electromagnetic radiation. In addition, a neutrino signal hasbeen found for SN1987A. Therefore, multi-messenger astronomy demonstrated itsefficiency for decades even before observations of the first gravitationalradiation sources. However, usually, one has only manifestations of black holesin a weak gravitational field limit and sometimes a model with a black holecould be substituted with an alternative approach which very often looks muchless natural, however, it is necessary to find observational evidences toreject such an alternative model. After two observational runs the LIGO-- Virgocollaboration provided a confirmation for an presence of mergers for ten binaryblack holes and one binary neutron star system where gravitational wave signalswere found. In addition, in last years a remarkable progress has been reachedin a development of observational facilities to investigate a gravitationalpotential, for instance, a number of telescopes operating in the Event HorizonTelescope network is increasing and accuracy of a shadow reconstruction nearthe Galactic Center is improving, meanwhile largest VLT, Keck telescopes withadaptive optics and especially, GRAVITY facilities observe bright IR stars atthe Galactic Center with a perfecting accuracy.

Tests of gravity theories with Galactic Center observations