A variety of organomolybdenum and organorhenium complexes, most prominently methyltrioxorhenium(VII) (MTO), are applicable as efficient and selective oxidising agents in the presence of organic hydroperoxides (molybdenum complexes) or hydrogen peroxide (rhenium complexes). Besides strictly homogeneous oxidation catalysis, there is increasing interest in immobilizing homogeneous catalysts, both on carrier materials and in ionic liquids. Several methods that differ mainly in the anchoring mode and the nature of the supporting material have been described, and the resulting materials were applied to oxidation catalysis. Chiral oxidation catalysis with the compounds mentioned in the title is still in its infancy, but initial results point towards a promising future. The supported catalysts combine properties of homogeneous catalysts (reactivity, control and selectivity) and heterogeneous catalysts (enhanced stability and reusability). Homogeneous catalysts have a clearly defined composition, and mechanistic examinations are usually less problematic than with bulk (heterogeneous) catalysts, where the active sites are less clearly defined. It is also more straightforward to modify homogeneous catalysts by fine-tuning their ligand environments.