This review summaries recent patents on catalysts dealing with quasicrystal. Icosahedral quasicrystal (iQc) Al-Cu-Fe has been studied in terms of catalysis. The Al63Cu25Fe12 iQc (i-AlCuFe) is a promising precursor for Cu catalysts, whose constituent elements, compositions and quasi-periodic structure are in favor of processing high performance catalysts. Brittleness resulting from quasi-periodic structure enables one to obtain powder form for processing catalysts. Relatively low dissolution rate of Al due to quasi-periodic structure upon leaching with NaOH solution, generates homogeneous nanocomposite consisting of Fe3O4 and Cu and hence gives rise to high activity and thermal stability for steam reforming of methanol. The catalytic properties of the leached i- AlCuFe are furthermore improved by formation of a spinel CuFe2O4 generated by consequent calcination at 873K in air. In order to understand sole contribution, spinel CuFe2O4 is studied independent of i-AlCuFe. Bulk spinel CuFe2O4 reduced at 633K shows a self-assembled microstructure with fine dispersion of Cu nanoparticles embedded in porous Fe3O4 matrix, accompanied by high catalytic performance. High thermal stability of Cu nanoparticles in the Fe3O4 is ascribed to the immiscible interaction between Cu and Fe, where the Fe3O4 can suppress the sintering of Cu particles.