In the current review paper, the N2O direct decomposition was investigated over a series of different catalytic systems, containing metals, zeolites, cobalt spinels. The N2O split via catalysis and the use of membrane systems in the separation to molecules N2 and O2 were studied, too. Decomposition of N2O has been studied in the temperature rate of 673 to 873 K over supported catalysts of chemical elements: Pd, Rh, Ru, Ni, Pt, Zn, Fe, Cu, Ir, over γ- Al2O3 showing their best catalytic activity. M-zeolites, (M = Cu, Fe, Co, etc.) supported on perovskite or precious metals such as Pd, Rh zeolites and dominant iron and copper catalytic structures such as ZSM-5, MFI, BEA, BETA investigated in the temperature rate of 583 to 775 K with best catalytic activity. Iron zeolites are more prevalent at high concentrations showing good catalytic behavior only at high temperatures. The spinel catalyst Zn0.36Co0.64Co2O4 and Rh/Mullite catalyst offer up to complete N2O conversion.