Natural gas (NG) is a suitable alternative to gasoline and diesel fuels to decrease the carbon footprint of the mobility and energy sectors. Although NG is considered a fossil fuel, methane (CH4), its main component, can be produced industrially from power-to-gas processes (syngas) and wet biomass (biogas). Hence, if in the future CH4 is predominantly produced via these routes, it will become a carbon-neutral fuel. Nonetheless, because CH4 is a severe greenhouse gas, its emissions will be continuously more stringently regulated by the European emission standards. Therefore, efficient catalytic exhaust after-treatment technologies need to be developed to prevent NG from being ignored in future energy scenarios. NG can be used for many applications, such as fuel for natural gas vehicles (NGVs), electricity generation, domestic heating, or even coupling to endothermic reactions. However, since the transportation sector contributes up to 20 % of the global air emissions, this thesis focuses on the removal of CH4 from the exhaust of engines fuelled with NG and operated under lean-burn and stoichiometric conditions. Unburnt CH4 is typically removed from the exhaust gas using palladium-based catalysts, which suffer from thermal deactivation as well as water and sulphur poisoning. Catalyst deactivation can be countered either by improving the material formulation and properties or by tuning the operating conditions. In the latter case, evidence exists that periodic changes in the reaction conditions can mitigate the deactivation processes and even enhance CH4 oxidation, thus decreasing the emission levels. For NGV applications, this could be accomplished by periodic variations of the O2 concentration (lean/rich O2 pulses) in the reactive feed. This thesis work aims at demonstrating and proposing strategies for the improvement of CH4 abatement from lean-burn and stoichiometric NG engines through periodic operation while understanding at a fundamental level the behaviour of the active metals (oxidation state and surface structure) using spectroscopic tools. First, the beneficial effect and structural modifications induced by repeated short reducing pulses (SRP; O2 cut-off for 3 s every 5 min) were studied on a Pd/Al2O3 catalyst for wet lean methane oxidation (cf. lean-burn NG engines; Chapter 3). Under these conditions, we were able to activate the catalyst and bring it to a highly active state compared to static reaction conditions. This strategy also allowed reversing the structural effects induced by thermal and hydrothermal treatments and therefore recovering the degraded activity of these materials. Under isothermal conditions (435 °C), SRP suppressed the fast deactivation of Pd/Al2O3 (fresh and aged) observed under static conditions in the presence of water and allowed to maintain the catalyst active (> 99% CH4 conversion) over long times. The combination of time-resolved operando X-ray absorption spectroscopy (XAS) data and kinetic models of Pd oxidation showed that under static conditions only moderately active PdO species are present, while during SRP operation an amorphous PdOx shell around a metallic Pd core is formed repeatedly. We observed that as long as the Pd0 core is present, high activity could be achieved. However, once the Pd0 core is fully consumed, PdOx is believed to densify and crystallize causing a decrease in CH4 conversion. Such deactivation could be reversed as well by SRP. These findings allowed us to propose a pra