Fixation of dinitrogen into ammonia is an essential biological process for the evolution of life, and at the same time ammonia is an essential component for many industrial processes, including fertilizers, plastics, and so on. NH 3 is also known as the best alternative to H 2 in fuel cells. However, due to chemical inertness, direct conversion of N 2 into NH 3 is not possible; a suitable catalyst is required. The century-old Haber−Bosch process, utilizing an Fe-based catalyst, is extremely energy-intensive and eco-unfriendly due to the consumption of fossil fuels. In recent years, huge development has taken place in the design and applications of suitable electro-and photocatalysts for artificial N 2 fixation. First-principles calculations have been considered as a powerful avenue for theoretical screening of promising catalysts through rational design and analysis of the plausible mechanisms or pathways of reactions. The present review focuses on recent theoretical developments of various unsupported nanoclusters and supported single-atom and cluster catalysts for application in electro-and photochemical N 2 reduction reactions. The support substrates include oxides, carbides, nitrides of metal-based 2D materials, porous carbonaceous materials, and metal-free 2D materials containing main-group elements like B, C, N, and P. Although some reviews have already been made, focusing on the research related to either electro-or photocatalytic N 2 fixation on different catalysts, here we give a comprehensive account of both electrochemical and photochemical nitrogen reduction reaction (NRR) activities and selectivities of various supported single-atom and polyatomic cluster catalysts. Additionally, a comparative assessment is made on the basis of free energy of adsorption, most favorable pathway, potential limiting step, and corresponding limiting potential of the NRR.