Polymer supported metal complex catalysts and methods of their preparation and use are described. The polymer supported metal complex catalysts can be obtained via ligand exchange reactions between polymer ligands and a metal complex having catalytic activity. For example, a polymer supported rhodium (II) complex catalyst can be prepared via ligand exchange reaction between an insoluble polymer and a rhodium (II) carboxylate complex, wherein the insoluble polymer is prepared by a copolymerization reaction of (i) a styrene derivative with a substituted carboxylic acid, (ii) a styrene, and (iii) a linear alkane with both ends substituted by vinylbenzyloxy groups. The polymer supported catalysts can be used to catalyze asymmetric carbene reactions such as C—H insertion reactions and the like with high catalytic activity, chemical selectivity, diastereoselectivity, and enantioselectivity.