The structural chemistry of Co-Mo-alumina hydrodesulfurization catalysts has been critically reviewed in this article. The location and nature of cobalt in the sulfided catalysts has been discussed. Small MoS2, crystallites (10 to 30 Å) that occur on the surface of a sulfided sample are unstable due to the high, net negative charge on the sulfur ions on their edges. They incorporate cations like Co2+ at the edges of the MoS2sheet (not intercalated between the sheets) and attain stability. It is shown that for the range of crystallito sizes of MoS, in these systems, a maximum of one Co ion can be incorporated per two Mo ions in this manner. Cobalt thus lends structural stability to the MoS2, crystallites and suppresses the excessive formation of anion vacancies at crystallite edges. Molybdenum sulfide crystallites on sulfided Mo-A12O3, lacking this stabilizing influence of cobalt, lose excess sulfur, leading to the creation of a larger concentration of multiple anion vacancies at their edges. The presence of these strongly acidic multiple vacancies, however, leads to a lower structural stability of these crystallites. Moreover, these strongly acidic sites are also deactivated faster in the presence of unsaturated molecules (like diolefins, olefins, etc.), accounting for the fact that the superiority of Co-Mo-Al2O3over Mo-Al2O3manifests itself mainly in the steady-state activity [61–63].