The known tetrathiometalates MoS42-/3-, WS42-/3-, ReS4-/2-/3-, and the unknown species TcS4-/2-, RuS40/-, and OsS40/-/2- were calculated using ab initio and DFT methods. The one-electron reduced species with d(1) configuration were shown to exhibit a slight Jahn-Teller distortion (T-d --> D-2d); the largest corresponding stabilization energy was obtained for MoS43- with -4.17 kcal/mol. Trends in vacuum bonding energies involve a destabilization on going from 5d(n) to 4d(n) systems and on reduction froth d(0) to d(1) species, with the exception of Ru and Os complexes where the d(1) configurations are more stable than the d(0) forms. The d(2) species ReS43- and OsS42- have vacuum bonding energies similar to those of d(1) analogues: The metal contribution to the lowest unoccupied MO (e) of d(0) forms is lowest for the neutral RuS4 and OsS4 and highest for the dianions MoS42- and WS42-. The DFT approach supported by correlated ab initio calculations describes the main features of the electronic spectra of the d(0) complexes. For the experimentally best accessible ReS4n- system the absorption energies and stretching frequencies were well reproduced, and the related but hitherto unknown OsS4- ion is predicted to be a fairly stable paramagnetic species.