Concerns about emissions of carbon dioxide have created a need to develop more fuel-efficient vehicles. Diesel engines are generally more efficient than gasoline engines but improvements in the latter can be achieved by operating under lean-burn conditions. With both diesel and lean-burn gasoline engines, the nitrogen oxides are emissted under oxidising conditions. It is scientifically very challenging to reduce nitrogen oxides under oxidising conditions. After a short survey of conventional three-way catalysts, and the associated fundamental aspects of NOx reduction under stoichoimetric conditions, this review focuses on the knowledge and know-how that has been developed for lean engine emission control. Early research on hydrocarbon selective catalytic reduction on zeolite, oxide, and metal-based systems is examined, and some of the key mechanistic models are described. Since none of these systems are of sufficient activity and stability to satisfy current legislation attention has turned to NOx storage and reduction systems. The basic principles of these are described, and the present state of knowledge regarding the mechanisms of storage and regeneration are discussed. The many apparent discrepancies are highlighted and an attempt is made to rationalise the current state of knowledge by taking into account the varying experimental conditions reported nit he literature. For diesel engines, NOx storage and reduction is not an ideal solution and so the final section of this review is concerned with silver-based catalysts and especially with the dramatic effect of small amounts of hydrogen on the efficiency of these catalysts for hydrocarbons selective catalytic reduction.