A detailed reaction mechanism is proposed for the formation of crystalline elemental sulfur from aqueous sulfide by oxidation with transition-metal ions like V-V, Fe-III, Cu-II, etc. The first step is the formation of HS. radicals by one-electron oxidation of HS- ions. These radicals exist at pH values near 7 mainly as S-.-. Their spontaneous decay results in the formation of the disulfide ion S-2(2-). The further oxidation of disulfide either by S-.- radicals or by the transition-metal ions yields higher polysulfide ions from which the homocyclic sulfur molecules S-6, S-7, and S-8 are formed. In water these hydrophobic molecules form clusters which grow to droplets of liquid sulfur (sulfur sol). Depending on the composition of the aqueous phase, crystallization of the liquid sulfur as either alpha- or beta-S-8 is rapid or delayed. Surfactants delay this solidification, while certain cations promote it. All these reactions are proposed to take place in desulfurization plants working by the Stretford, Sulfolin, Lo-Cat, SulFerox, or Bio-SR processes. In addition, the sulfur produced from sulfide by oxidizing sulfur bacteria is formed by the same mechanism, which now explains many observations made previously (including the formation of the byproducts thiosulfate, polythionates, and sulfate).