Earth-abundant and nontoxic sulfur (S) is emerging as a key element for developing new materials for sustainable energy. Knowledge gaps, however, still remain regarding the fundamental properties of sulfur especially on a theoretical level. Here, a comprehensive first-principles study has been performed to examine the predicted structural, elastic, phonon, thermodynamic, and optical properties of α-S₈ (α-S) as well as energy-related sulfides. A variety of exchange–correlation (X–C) functionals and van der Waals corrections in terms of the D3 method have been tested to probe the capability of first-principles calculations. Comparison of predicted quantities with available experimental data indicates that (i) the structural information of α-S is described very well using an improved generalized gradient approximation of PBEsol; (ii) the band gap and dielectric tensor of α-S are calculated perfectly using a hybrid X–C functional of HSE06; (iii) the phonon and elastic properties of α-S are predicted reasonably well using for example the X–C functionals of LDA and PBEsol, and in particular the PBE + D3 and the PBEsol + D3 method; and (iv) the thermodynamic properties of α-S are computed accurately using the PBEsol + D3 method. Examinations using Li₂S, CuS, ZnS, Cu₂ZnSnS₄ (CZTS), SnS, Sn₂S₃, SnS₂, β-S₈ (β-S), and γ-S₈ (γ-S) validate further the crucial role of the van der Waals correction, thus suggesting the X–C functionals are PBEsol + D3 and PBE + D3 (and PBEsol in some cases) for sulfur as well as S-containing materials. We also examine the possibility by using the Debye model to predict thermodynamic properties of unusual materials, for example, α-S. In addition, the bonding characteristics and non-polar nature of α-S have been revealed quantitatively from phonon calculations and qualitatively from the differential charge density.