In general, a catalyst is used to enhance the reaction and to complete the reaction quickly or accelerate the reaction involving reactants and catalysts. In the catalysis process, only the chemical structure of reactant changes with time, but the structure of the catalyst remains unaffected throughout the course of the reaction. The varieties of chemicals that can be used as a catalyst in numerous chemical reactions are metals, acids, bases, organic compounds, inorganic complexes, enzymes and polymers. Some specific polymers have the ability to catalyse reactions with the formation of carbon-carbon and carbon-non carbon linkages. Polyvinyl pyridine and sulfonated polystyrene are very useful and simple polymers that can act as catalysts. The catalytic activity of polymers is pronounced due to modification in polymer chains. Further, polymers may also be used as a support for another catalyst. Polymer catalysis can be illustrated with soluble linear polymers, ion exchange resins, polymer-supported phase transfer catalysts, palladium catalysts on polymer supports, etc. The brief review of each is explained by citing important examples along with their basic principles.