The present article consists a critical up-to-date review of the research conducted so far on the selective catalytic reduction of NOx with hydrogen under lean-burn conditions as an alternative technology to the existing NH3- and HC-SCR. Noble Metal based catalysts are described in detail with emphasis on the analysis of the various reaction mechanisms that have been put forward in the literature. The influence of the nature of the support chemical composition and the preparation method and structure of the catalysts on the reaction mechanism is also discussed. Finally, the effects of various reaction parameters on the catalysts activity, selectivity and stability with reaction time are discussed in detail.