Using the 22-meter RT-22 radio telescope (Simeiz), a unique database on the variability of active galactic nuclei (AGN) in the centimeter and millimeter wavelength ranges has been created. This database is virtually the only one of its kind in the world in this frequency range. A special class of AGNs has been identified—tight binary systems of supermassive black holes (SMBHs) at an evolutionary stage close to merger, exhibiting quasi-periodic variability in their emission. Statistical analysis indicates that, due to beaming effects, only about 1% of such systems are observable. We present results of long-term, multi-frequency radio monitoring of several AGNs suspected of harboring binary SMBHs: 3C 273, 3C 454.3, S5 0528+134, and AO 0235+164. Based on these observations, a new model is proposed for estimating the parameters of tight binary SMBHs solely from radio data. An energy balance analysis demonstrates that standard accretion onto a single SMBH cannot account for the observed emission power. An alternative model is proposed, in which the primary energy release is caused by the secondary SMBH traversing a common accretion environment. The methodology for determining the physical parameters of the SMBHs includes harmonic and wavelet analyses, as well as estimation of companion masses and orbital parameters. The results suggest that these systems may consist of extremely massive and compact binaries with nearly equal-mass components. The most massive binary black hole (3C 454.3) and the most powerful radio emitter in the Universe (S5 0528+134, "Nimfa") have been identified. For the first time in global practice, the phenomenon of giant flares of water maser emission in Galactic sources has been discovered using the RT-22 radio telescope of the Crimean Astrophysical Observatory. We present the results of long-term monitoring of water kilomasers in the Galactic sources IRAS 18316–0602 and W51 Main at the 22.35 GHz line. It has been established that IRAS 18316–0602 is the most powerful water kilomaser in the Galaxy. This discovery was included in the annual report of the Russian Academy of Sciences to the President of the Russian Federation as one of the most significant astrophysical achievements of 2019. Such results have been obtained for the first time in the global scientific community. A methodology has been developed to estimate the level of gravitational radiation from tight binary SMBHs and compact binary stellar systems. The flux of gravitational waves reaching the Earth from such sources has been estimated, showing that it is potentially detectable by gravitational wave detectors such as the International Pulsar Timing Array (IPTA). This opens up new broad possibilities for further research of gravitational waves with the aim of their experimental detection.