Binuclear transition-metal complexes based on conjugated systems containing coordinating functions are potentially suitable for a wide range of applications, including light-emitting materials, sensors, light-harvesting systems, photocatalysts, etc., due to energy-transfer processes between chromophore centers. Herein we report on the synthesis, characterization, photophysical, and theoretical studies of relatively rare rhenium(I) and rhenium(I)-iridium(III) dyads prepared by using the nonsymmetrical polytopic ligands (NN2 and NN3) with the strongly conjugated phenanthroline and imidazole-quinoline/pyridine coordinating fragments. Availability of these different diimine chelating functions and targeted synthetic procedures allowed one to obtain a series of mononuclear (Re and Ir) and binuclear (Re-Re and Re-Ir) metal complexes with various modes of {Re(CO)3Cl} and {Ir(NC)2} metal fragment coordination. The obtained compounds were characterized by 1D 1H and 2D (COSY and NOESY) NMR spectroscopy, mass spectrometry, elemental analysis, and X-ray diffraction crystallography. The photophysical study of the complexes (absorption, excitation and emission spectra, quantum yields, and excited-state lifetimes) showed that their emission parameters display strong dependence on the manner of metal center coordination to the diimine bidentate functions. The mononuclear complexes with an unoccupied imidazole-quinoline/pyridine fragment [Re(NN2), Re(NN3), and Ir(NC2)2(NN2)] or those containing a coordinated {Ir(NC)2} fragment in this position [Ir(NC2)2(NN1) and Re(NN2)Ir(NC1)2-Re(NN2)Ir(NC4)2] exhibit moderate-to-intense phosphorescence (quantum yields vary from 3% to 56% in a degassed solution), whereas the complexes containing a {Re(CO)3Cl} moiety in the imidazole-quinoline/pyridine position [Re2(NN2), Re2(NN3), and Ir(NC2)2(NN2)Re] demonstrate a strong reduction in the phosphorescence efficiency with a quantum yield of ≪0.1%. Quenching of the phosphorescence in the latter types of emitters is discussed in terms of a strong decrease in the radiative rate constants for these complexes compared to their analogues mentioned above, while the nonradiative constants remain nearly unchanged. Theoretical density functional theory (DFT) and time-dependent DFT (TD DFT) calculations, including evaluation of the radiative rate constants for the couple of structurally analogous complexes with and without a {Re(CO)3Cl} moiety coordinated to the imidazole-quinoline/pyridine chelating function, confirmed the observed trend in the variation of the emission intensity.