This is a review of the published papers that focus on the reactivity of carbonyl complexes of molybdenum in low oxidation states (usually zero or two) and possible applications of molybdenum complexes as precursors of catalysts in different reactions of unsaturated organic substrates such as alkenes and alkynes. The following reactions are analyzed: metathesis, metathesis polymerization, free radical reactions of alkenes, hydrogenation, hydrosilylation, hydrogermylation, hydrostannation, hydroarylation, asymmetric allylic alkylation, and epoxidation. In addition to the interesting practical aspects of these catalytic reactions, they provide additional insights into molybdenum chemistry. Keywords: Metathesis, hydrogenation, hydrosilylation, hydrogermylation, hydrostannation, hydroarylation, asymmetric allylic alkylation, epoxidation, bidentate phosphine ligands, diphenylphosphinomethane (dppm), diphenylphosphinoethane (dppe), diphenylphosphinopropane (dppp), molybdenum carbonyl complexes, hydrostannation reaction