The electronic structure of α-V₂O₅, γ′-V₂O₅, and γ-MeV₂O₅ (Me = Li, Na) bronzes is studied by quantum-chemical calculations completed by spectroscopic experiments. The calculations are performed using the G₀W₀ method with the DFT+U self-consistent wave function as an initial approximation. The electronic band gap E_g = 2.89 eV calculated for α-V₂O₅ is found to be in fair agreement with available experimental data. The strategy was then applied to studying the electronic structure of the γ′-V₂O₅ phase and γ-MeV₂O₅ bronzes for which no experimental band gap data exist in the literature. Computed E_g values are equal to 3.17, 1.21 and 1.18 eV for γ′-V₂O₅, γ-LiV₂O₅, and γ-NaV₂O₅, respectively. The nature of the alkali metal atom is determined to have little influence on the structure and electronic states of the bronzes. Raman spectra recorded with different wavelengths of exciting radiation have allowed the determination of the energy threshold corresponding to the transition from off-resonance to resonance Raman scattering process. In this way, a band gap value in the range 2.54-2.71 eV for α-V₂O₅ and γ′-V₂O₅ is obtained in good agreement with the experimental values for the α-phase. Raman spectra of γ-MeV₂O₅ suggest the band gap smaller than 1.58 eV in these materials, whereas the photoluminescence measurements yield E_g ≈ 0.95 eV for the γ-LiV₂O₅ bronze. Remarkably, the result of the G₀W₀ calculations lies in between the experimental estimates. The strong similarity of structures and electronic states of γ-LiV₂O₅ and γ-NaV₂O₅ accounts for their the same operating voltage when used as cathodes in Li(Na)-ion batteries.