This article provides a comprehensive review and evaluation of the selective catalytic reduction (SCR) of nitrogen oxides (NO X) using ammonia as a reducing agent in flue gases produced by the combustion of hydrogen or ammonia with air. Over the years, density functional theory calculations (DFT) have been used extensively to complement experimental results, with emphasis on understanding adsorption modes and reaction mechanisms. Recent advances in this field have led to a shift from non-periodic to more accurate periodic models. It has been shown that the SCR reactions mainly follow the Eley-Rideal mechanism, with NH 2 NO identified as the most important intermediate. Global kinetic and microkinetic models are widely used, but these models often overlook the crucial role of adsorption of water molecules on catalyst surfaces. Consequently, their utility is reduced under conditions of elevated water vapor concentrations. To address this limitation, numerical fluid dynamics simulations (CFD) have been introduced that include user-defined functions to model chemical deNO X reactions. In particular, the method CFD can also take into account the adsorption of relevant species at the active sites of the catalyst. We highlight a significant knowledge gap in the existing literature: the lack of consideration of the adsorption of water on catalyst surfaces during the selective catalytic reduction of NO X. Consequently, these models are inadequate for flue gases with high water vapor content produced during the combustion of hydrogen or ammonia. Addressing this shortcoming is critical to better understand and accurately predict the performance of SCR under different operating conditions. [Display omitted] • Environmental aspects of carbon-free fuel combustion products are identified. • Selective catalytic reduction of NO x (SCR deNO X) of carbon-free fuels is addressed. • Existing DFT, kinetic modelling and CFD studies are summarized. • Water vapor inhibition of NH 3 -SCR deNO X is barely considered. • Multi-scale modelling would significantly improve the understanding of NH 3 -SCR deNO X. [ABSTRACT FROM AUTHOR]