The Meerwein-Ponndorf-Verley (MPV) transfer hydrogenation of aldehydes and ketones to the corresponding alcohols is distinguished by its exceptional chemoselectivity. This reaction is particularly suited for the reduction of unsaturated aldehydes and ketones, compared to catalytic reductions with molecular hydrogen using noble metal catalysts. The MPV reaction has traditionally been carried out using homogeneous catalysts like aluminium or titanium alkoxides. However, over the past two decades, an increasing number of reports on heterogeneous catalysts for the MPV reaction have been published. This interest is stimulated by the advantages of heterogeneous over homogeneous catalysis, particularly for larger-scale applications. The article provides a critical review of the recent literature on heterogeneous catalysts for the MPV reaction. The materials include hydrotalcites, metal oxides such as magnesium oxide, zirconia, silica and alumina, alkoxides of Al, La, Zr and Hf grafted to high surface area mesoporous materials, and zeolites. In particular, zeolite beta has been found to be a highly stereoselective catalyst in the MPV reduction of 4-tertbutylcyclohexanone, giving predominantly cis-4-tert-butylcyclohexanol rather than the thermodynamically stable transalcohol. The activity was improved with the incorporation of other metals such as Ti, Sn and Zr. These materials show good tolerance to moisture, lack of leaching and ease of regeneration, thus making them useful catalysts in MPV reduction. The activity of a catalyst depends on its ligand exchange capability with the reductant with a high ligand exchange rate enabling the use of catalytic amounts.