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Nitrous oxide (N2O) is both a pollutant and a potentially valuable oxidant. Its abatement is critical because of its high global warming potential, while its activation may enable efficient partial oxidation of methane (CH4). This thesis addresses N2O abatement and utilization, moving from challenges related to NH3-engines toward active-site identification, structure-activity relationships, and reaction mechanisms. Fe-exchanged zeolites emerged as promising catalysts for N2O abatement above 400°C, but inhibition by O2, H2O, and NH3, together with hydrothermal deactivation under ca. 30 vol% H2O highlighted the need for catalysts active at lower temperatures (Chapter 2). Co3O4-based materials modified with a second element and promoted with Rh were investigated for direct N2O decomposition. Co-Al-Rh showed the highest activity, with a ca. 38-fold rate increase relative to its Rh-free analogue and the lowest light-off temperature (ca. 190°C). Its performance was linked to improved redox properties, weakening of the Co-O bond, and increased oxygen mobility (Chapter 3). Hence, a Rh/Co3O4-CeO2 catalyst was engineered, for which operando modulated excitation XAS revealed a cooperative Mars-van Krevelen pathway sustained by RhOx redox cycling (Chapter 4). The second addresses Fe-exchanged zeolites for N2O decomposition and CH4 oxidation to CH3OH. Because isolated Fe ions, clusters, and nanoparticles coexist, a multi-modal operando spectroscopic approach was adopted by combining UV-vis, DRIFTS, EPR, XAS, XES, and RIXS, often coupled with modulated excitation. Applied to Fe-CHA during N2O decomposition, this approach revealed an Fe2+ -> Fe3+O -> Fe3+OH redox sequence, with the reduction half-cycle identified as the rate-determining step. Correlation of spectroscopy-derived kinetics with catalytic rates assigned the N2O decomposition reactivity to monomeric Fe ions in six-membered rings of the CHA framework (Chapter 5). In Ar, only isolated axially coordinated Fe2+ species participate in N2O decomposition, whereas under reducing conditions additional Fe species become redox-active. These insights were enabled by a modulated-excitation-aided step-scan EPR methodology, which improved the temporal resolution of EPR by an order of magnitude (Chapter 6). For N2O-assisted continuous CH4 hydroxylation over Fe-CHA, the reaction was shown to be site-selective and to involve monomeric Fe ions in six-membered rings undergoing a formal Fe2+/Fe3+ redox cycle. The data support a radical-rebound pathway in which N2O forms a highly reactive Fe3+Ooxo moiety, followed by CH activation and rebound chemistry leading to continuous CH3OH formation. The reversibility of the Fe3+-OH intermediate was directly associated with catalytic turnover (Chapter 7). Temperature governs the transition between catalytic and stepwise CH4 hydroxylation: at 275°C, Fe3+OH behaves as a dynamic intermediate consistent with continuous methanol production, whereas at 250°C, it loses its dynamic respon