The selective non-catalytic reduction (SNCR) process used to transform nitrogen monoxide molecules into environmentally friendly gases is reviewed with its numerical modeling. The fundamentals of SNCR in terms of chemistry and flow physics are first discussed, to then examine how they impact on the design and optimization of furnaces and incinerators relying on this technology. The various options in operation today are presented for coal-fired or waste-to-energy power plants, biomass and CO boilers. In complement, specific applications using additive components are discussed along with the amine reclaimer waste approach. The methodology and the challenges of computational fluid dynamics applied to SNCR systems are reviewed, before discussing emerging simulation techniques, as large eddy simulation (LES) of such complex systems. The modeling of the multicomponent evaporation of the liquid reagent injected for transforming NOx, as urea, and the modeling of the chemistry in the gaseous phase, are addressed for the numerical simulation of SNCR. Finally, reduced-order modeling of SNCR is discussed and perspectives are drawn for the control, in situ, of SNCR systems.