A polymer microgel is an intramolecularly cross-linked and discrete macromolecule, with the size ranging from nanometer to micrometer, to be fully dispersed, swollen, and soluble in various solvents (1-3), critically distinct from an insoluble macroscopic gel. The inner network structure of microgels provides multiple cavities with high loading capacity for various reagents. Focused on these features, microgels are so far employed for various applications, for example, as nanoreactors for catalysis, as nanocapsules (nanocarriers) for dye encapsulation, drug and gene delivery system, and as imaging agents (4-13).In this paper, recent advances in polymer-based microgels applicable to catalysis are comprehensively reviewed, especially focusing on the smart design of catalyst-embedded microgels and the unique catalytic performance.The study of these microgels began with the first report by Williams and co-workers in 1979 (14). They designed water-soluble microgels containing hydroxamic acid as a catalytic site by emulsion polymerization and discovered the excellent activity for the cleavage of 4-nitrophenylester. After the first example, several organic catalysts, such as acid (15,16), quaternary ammonium (17), and mercapto group (18), were incorporated into microgels. In the 2000s, polymer microgels with precisely controlled three-dimensional architectures have been combined with various catalyst species: metal complexes (19), metal nanoparticles (20), organocatalysts (21), and enzymes (22). The movement is attributed to the recent advances in living polymerization systems (23-28) that are quite effective to control primary structures of polymeric materials (3,10-13).Typical objectives for the encapsulation of catalysts into microgels are to improve the stability and the recyclability, with high activity and selectivity comparable to nonsupported (original) counterparts. The compatible performance originates from one of the inherent properties of microgels, that is of being "solubilized and/or dispersed" gels. Generally, insoluble gel-supported catalysts, typically based on silica and polystyrene gels, are useful for convenient catalyst recycle and product recovery (29), whereas they often result in low activity owing to the less accessibility of substrates to catalysts by the small surface area. In turn, soluble (non-cross-linked) polymer-supported catalysts often suffer catalyst leaching from the scaffolds to products during reactions, to spoil product recovery and catalyst recycle, though they perform activity comparable to nonsupported (original) counterparts for first cycle (30). In contrast, soluble (or dispersed) microgels solidly enclose catalysts in the cross-linked networks, similar to