[en] We have studied, by means of first-principles calculations, the electronic and optical properties of the sulvanite family: Cu₃MX₄ (M  =  V, Nb, Ta and X  =  S, Se), which, due to its broad range of gaps and chemical stability, have emerged as promising materials for technological applications such as photovoltaics and transparent conductivity. To address the reliability of those properties we have used semi-local and hybrid functionals (PBEsol, HSE06), many-body perturbation theory (G₀W₀ approximation and Bethe–Salpeter equation), and time-dependent density functional theory (revised bootstrap kernel) to calculate the quasi-particle dispersion relation, band gaps, the imaginary part of the macroscopic dielectric function and the absorption coefficient. The calculated valence band maximum and the conduction band minimum are located at the R and X-points, respectively. The calculated gaps using PBEsol are between 0.81 and 1.88 eV, with HSE06 into 1.73 and 2.94 eV, whereas the G₀W₀ values fall into the 1.91–3.19 eV range. The calculated dielectric functions and absorption coefficients show that all these compounds present continuous excitonic features when the Bethe–Salpeter equation is used. Contrarily, the revised bootstrap kernel is incapable of describing the excitonic spectra. The calculated optical spectra show that Cu₃VS₄ and Cu₃MSe₄ have good absorption in the visible, whereas Cu₃NbS₄ and Cu₃TaS₄ have it on the near ultraviolet. (paper)