How thiols and disulfides bind to gold surfaces to form self-assembled monolayers is a long-standing open question. In particular, determining the nature itself of the anchor groups and of their interaction with the metal is a priority issue, which has so far been approached only with oversimplified models. We present ab initio calculations of the adsorption configurations (dissociative and not) of methanethiol and dimethyl disulfide on Au(1 1 1) at low coverage, which are based on density functional theory using gradient-corrected exchange-correlation functionals. A complete characterization of their structure, binding energies, and type of bonding is obtained. It is established that dissociation is clearly favored for the disulfide with subsequent formation of strongly bound thiolates, in agreement with experimental evidence, whereas thiolates resulting from S-H bond cleavage in thiols can coexist with the adsorbed "intact" species and become favored if accompanied by the formation of molecular hydrogen.