The main aim of this thesis is to understand the catalytic activity of transition metals and noble metals for the direct decomposition of NO and the oxidation of CO. The formation of NOx from combustion of fossil and renewable fuels continues to be a dominant environmental issue. We take one step towards rationalizing trends in catalytic activity of transition metal catalysts for NO decomposition by combining microkinetic modelling with density functional theory calculations. We establish the full potential energy diagram for the direct NO decomposition reaction over stepped transition-metal surfaces by combining a database of adsorption energies on stepped metal surfaces with known Brønsted–Evans–Polanyi (BEP) relations for the activation barriers of dissociation of diatomic molecules over stepped transition- and noble-metal surfaces. The potential energy diagram directly points to why Pd and Pt are the best direct NO decomposition catalysts among the 3d, 4d, and 5d metals. We analyze the NO decomposition reaction in terms of the Sabatier analysis and a Sabatier–Gibbs-type analysis and obtain an activity trend in agreement with experimental results. We show specifically why the key problem in using transition metal surfaces to catalyze direct NO decomposition is their significant relative overbinding of atomic oxygen compared to atomic nitrogen. We calculate adsorption and transition state energies for the full CO oxidation reaction pathway by the use of DFT for a number of transition and noble metals; Pt, Pd, Cu, Ag and Au, and for various structures; closed packed surfaces, stepped surfaces, kinked surfaces, and a 12 atom corner model of a larger nanoparticle. We show obtained linear scaling relations between adsorption energies of reaction intermediates and BEP-relations between transition energies and adsorption energies. We establish a simple kinetic framework within the Sabatier analysis and obtain trends in catalytic activity based on the descriptors EO and ECO. We show that gold nanoparticles are optimal catalysts for low temperature CO oxidation and Pt closed packed surfaces are optimal for high temperature CO oxidation. We show that the change in catalytic activity of the elemental metals changes with the coordination number of atoms at the active sites. This effect is shown to vi be electronic in nature, as low coordinated metal atoms, which bind reactants most strongly, have the highest energy metal d states.