This review deals with heterogeneous hydroformylation catalysts, specifically metal complexes fixed in an organic polymer structure. It describes the main catalyst synthesis methods, provides data on hydroformylation of unsaturated compounds (including asymmetric hydroformylation), and shows how those compounds can be used. The special focus is on the systematization of data on heterogeneous catalysts developed on the basis of porous organic polymers. Due to their porous structure, resistance to organic media and the high concentration of heteroatoms they contain, these materials can be considered promising for developing highly active, selective and stable heterogeneous catalysts for hydroformylation of unsaturated compounds, particularly higher linear olefins.