Density functional theory (DFT) calculations are employed to investigate the structural and electronic properties of bare tritungsten clusters (W-3, W3-, W-3(2-)) and tritungsten oxide clusters W3Ox-/0 (x = 1, 2). Generalized Koopmans' theorem is applied to predict the vertical detachment energies and simulate the photoelectron spectra (PES) for W3Ox- (x = 0-2) clusters. Extensive DFT calculations are performed in search of the lowest energy structures for both the anions and the neutrals. The bare tritungsten clusters are predicted to be triangular structures with D-3h ((3)A(1)'), C-2u ((2)A(1)) and D-3h ((1)A(1)') symmetry for W-3, W-3 and W-3(2-), respectively. For W3O- and W3O clusters, the oxygen atom occupies the terminal site, while the next added oxygen atom is found to be a bridging one in both W3O2- and W3O2 clusters. Molecular orbital analyses are carried out to elucidate the chemical bonding of these clusters and provide insights into the sequential oxidation from W3- to W3O2-. Partial sigma- and delta-aromaticity are revealed in the neutral W3 (D-3h (3)A(1)'), while the anion W-3(2-) (D-3h, (1)A(1)') possesses only delta-aromaticity.