Active galactic nuclei (AGN) are the brightest objects in the Universe and their brightness is mainly caused by accretion of matter onto supermassive black holes (SMBH). This is the common reason of the AGN activity. However, every AGN has differences and fine features, which are the subject of an intensive investigation. The occurrence of such highly-relativistic objects as SMBH residing at the AGN core makes them an excellent laboratory for testing the fundamental physical theories. The X-rays and gamma-rays generated in a corona of an accretion disc around SMBH yield valuable information for these tests, the radiation in the range of 1-100 keV being at present the most informative source. However, there are a number of obstacles for such a study due to different physical processes that complicate the interpretation of observations in different bands of the electromagnetic radiation. In this paper, we review the current concepts concerning the structure of AGNs with a focus on the central part of these objects that require relativistic theories for their understanding. The basic notions of the unified AGN schemes are considered; some modifications are reviewed. The paper contains the following sections. I. Introduction; II. Observational manifestations and classification of galaxies with active nuclei (II.A. Optical observations; II.B. Radio observations; II.C. X-ray data; II.D Infrared data; II.E. AGN anatomy with multywave data); III. AGN ``central machine''; III.A. Black holes; III.B. Accretion disc types; III.C. Corona; III.D. AGN unified scheme); IV. Simulation X-ray AGN spectra (IV.A. The power-law contimuum and the exponential cut-off; IV.B. The absorption of X-rays; IV.C. Reflection; IV.D. Fe K$_{lpha}$ line; IV.E. Spin paradigm); V. AGN as a laboratory to test the fundamental interactions (V.A. Strong gravitational fields; V.B. Dynamic dark energy near compact astrophysical objects.
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