The molecular and electronic structure of the spherical Keplerates [{(Mo^VI)Mo^VI₅O₂₁}₁₂(Mo^V₂O₄)₃₀]¹²⁻ (Mo₁₃₂) and [{(W^VI)W^VI₅O₂₁}₁₂(Mo^V₂O₄)₃₀]¹²⁻ (W₇₂Mo₆₀) has been determined, for the first time, using first-principles density functional theory (DFT) based methods including solvent effects. Computed geometric parameters are in very good agreement with X-ray data, whereas the electronic structure reveals the archetypal nature of polyoxometalates.