The problems in the use of rhenium compounds and supported mono-, bi-, and poly-metallic rhenium-containing catalysts for carrying out reactions involving the metathesis of alkenes and unsaturated functional compounds, the hydrogenation and dehydrogenation of hydrocarbons, the conversion of hydrocarbons and their industrial mixtures, and the hydrogenation of fractions comprising carboxylic acids and the products of the hydroformylation of synthetic aliphatic acid esters are examined. The characteristic features of the behaviour of platinum–rhenium/alumina catalysts under reforming conditions are described. The specificity of the action of rhenium heptasulfide in the hydrogenation reactions of condensed N-containing aromatic compounds and in the reductive C-alkylation of indoloisoquinoline by alcohols is noted. The bibliography includes 251 references.