Catalytic nitrate reduction is an important chemical process applicable in water treatment. The overall mechanism is unknown but this knowledge could aid in the design of cheaper, more active, more selective catalysts. This dissertation was geared towards providing fundamental understanding of the surface chemistry occurring in such systems. In this work we explored the reduction of the three experimentally observed intermediates, namely nitrous oxide, nitric oxide and nitrite.  We use Density Functional Theory models to contrast pathways for adsorption, decomposition, and hydrogenation of nitrous oxide on several Pd facets. We show that nitrous oxide adsorbs weakly to Pd surfaces and decomposes readily to molecular nitrogen and atomic oxygen at any coverage of preadsorbed atomic oxygen below saturation. Decomposition to atomic nitrogen and nitric oxide is similarly facile at low adsorbate coverage but N-NO bond breaking becomes increasingly difficult with increasing coverage. These observations help rationalize the observed selectivity of catalysts for nitrous oxide reduction to molecular nitrogen over ammonia. In the overall catalytic cycle surface atomic oxygen is reduced by adsorbed hydrogen. Ambient water is effective in catalyzing these hydrogenation steps. Density Functional Theory models were also used to contrast pathways for adsorption, decomposition and hydrogenation of nitric oxide. Simulations show that nitric oxide adsorbs strongly to palladium surfaces. Water-mediated hydrogenation to NOH has the smallest barrier of all nitrous oxide reactions and is therefore the most likely first step.  The NOH reaction with the smallest barrier is the water-mediated hydrogenation to atomic nitrogen and water. The atomic nitrogen can then proceed to ammonia or nitrous oxide. Atomic nitrogen is hydrogenated to NH and NH2 to ammonia with the help of water molecules. However, direct hydrogenation of NH to NH2 is preferred over water-mediated pathways. Nitrous oxide is most likely formed by reaction of NH with nitric oxide followed by water assisted deprotonation.  One implication of this work is that there might be some ratio of nitric oxide: hydrogen binding energy which will allow high nitric oxide coverage for desired selectivity as well as sufficient hydrogen adsorption for reaction.