The nature of the interaction of water with the WO surface is of crucial importance for the use of this semiconductor oxide in photocatalysis. In this work, we investigate water adsorption and dissociation on both clean and O-deficient (001) WO surfaces by means of an accurate DFT approach. The O vacancy formation energy (computed with respect to O) has been evaluated for all possible surface configurations, and the removal of the terminal O atom along the c axis is found to be preferred, costing about half the corresponding energy in the bulk. The presence of oxygen vacancies leads to a semiconductor to metal transition, confirming the experimental evidence of n-type conductivity in defective WO films. HO preferably adsorbs on WO in a molecular undissociated form, due to the presence of W ions at the surface that act as Lewis acid sites. This interaction, about -1 eV per HO molecule, is not very strong. Contrary to what is usually expected, the presence of oxygen vacancies does not significantly affect HO adsorption. Finally, we investigated the HO desorption from a hydroxylated surface. This suggests that the exposure of WO to H directly results in a hydroxylated surface and the corresponding HO desorption turns out to be a very efficient mechanism to generate a reduced oxide surface, with important consequences on the electronic structure of this oxide.