In this review, we consider the reactions of NOx(x = 1, 2) with the nitrogen hydrides NH, NH2and NH3The reactions are relevant to the post-combustion, non-catalytic reduction of NOxwith NH3in the thermal de-NOxprocess and with HNCO in the rapid reduction of NOxas well as to the thermal decomposition of some high-energy materials, including ammonium dinitramide. The practical importance has motivated considerable theoretical interest in these reactions. We review numerous ab-initio molecular orbital studies of potential energy surfaces for NOx+ NHyand theoretical calculations of their kinetic parameters, such as thermal rate constants and branching ratios of various products. The most advanced theoretical calculations are carried out using the Gaussian-2 family of methods which provides the chemical accuracy (within 2 kcal mol-1) for the energetics and molecular parameters of the reactants, products, intermediates and transition states. We present a detailed comparison of the theoretical results with available experimental data. We show that the reactions of NOxwith NH and NH2are very fast because they occur without a barrier and lead to the formation of multiple products which include radicals and stable molecules. The reactions of NOxwith NH, taking place by the H abstraction to form NH and HNOxare slow but still relevant to the NH3de-NOxsystem, because of their fast reverse processes which have not yet been measuredexperimentally.