Catalytic CO oxidation is one of the most extensively studied reactions. The interest in this reaction can be explained by two main reasons: a) catalytic CO oxidation is of great practical importance in automotive exhaust gas control, air purification, and H2 purification for proton exchange membrane fuel cells (i.e., preferential CO oxidation (PROX)); b) CO oxidation is a simple model reaction that can provide insights into the nature of active sites of catalysts and mechanisms of catalytic processes. Cobalt oxide materials are promising catalysts for CO oxidation and PROX. Although many efforts have been made to explore the potential of cobalt oxide catalysts for the CO oxidation reaction, the nature of the active sites and the reaction mechanism are still not well understood. Open questions and contradicting results concern, for instance, the role of Co2+/Co3+, different oxygen species, oxygen vacancies, the role of promoters, formation of carbonates, influence of pretreatment, and catalyst deactivation. Therefore, the goal of this thesis was to gain mechanistic understanding of cobalt oxide and promoted cobalt oxide catalysts for CO oxidation and preferential CO oxidation reactions. For this purpose, a combined operando approach was employed: Fourier transform infrared spectroscopy (FTIR), near atmospheric pressure X-ray photoelectron spectroscopy (NAP-XPS), X-ray diffraction (XRD), and X-ray absorption spectroscopy (XAS) were used to monitor surface and bulk changes of catalysts under reaction conditions (CO and O2: CO, O2 and H2), in CO atmosphere and upon switching from CO to O2. The (near)surface composition of cobalt oxide under reducing (CO) and oxidizing (O2) atmospheres was studied first. Using synchrotron-based in situ NAP-XPS, including depth profiling by photon energy variation, and near-edge X-ray absorption fine structure (NEXAFS) at the Co L3,2 edge (total electron yield detection), the (near)surface electronic and structural changes of Co3O4, adsorbates and oxygen vacancies evolution during CO reduction and subsequent O2 reoxidation were monitored. The results obtained by combining information from different information depths allowed to distinguish surface vacancy formation during reduction of Co3O4 in CO atmosphere (RT-150 oC) from the oxygen vacancies created by mobility of bulk lattice oxygen (200-250 oC). Additionally, formation of a mixed phase of rocksalt-type CoO and metastable wurtzite-type CoO in the near-surface ( 3-5 nm) during reduction of Co3O4 in CO atmosphere at 250 oC were identified. Moreover, the obtained data revealed that the temperatures for reduction of cobalt oxide and the reoxidation of metallic cobalt did not coincide. This provides new insights into the surface chemistry of Co3O4 and shed light on the CO oxidation mechanism on cobalt oxide, as well as the deactivation and regeneration of metallic cobalt Fischer-Tropsch catalysts under oxidizing conditions. CO oxidation over cobalt oxide catalysts by means of operando techniques was studied next. Operando FTIR, NAP-XPS, XRD, and XAS were employed to monitor surface and bulk changes in the catalyst under static reaction conditions (CO and O2), in CO atmosphere and upon switching from CO to O2. Operando NAP-XPS revealed fully oxidized Co3O4 during CO oxidation up to 200 oC, whereas in (pure) CO the surface reduction of Co3O4 started around 100 oC. Significant changes in the Co3+/Co2+ ratio were observed upon switching from CO to O2: 25% Co3+ in CO vs 28% Co3+ in O2 at 150 oC; and 24% Co3+ in CO vs 28% Co3+ in O2 atmosphere at 200 oC. In the C 1s region, carbonates, molecular CO adsorbed on cobalt cations, and elementary carbon were observed, the latter indicating CO dissociation during CO oxidation. FTIR spectroscopy clearly showed that CO formed surface carbonate species with Co3O4 (i.e., monodentate and at higher temperatures bidentate), while during the reaction the amount of carbonates decreased. The combined results of operando NAP-XPS and operando FTIR spectroscopy (i.e., static steady-state and dynamic switching experiments) indicate a redox Mars-van-Krevelen mechanism of CO oxidation on Co3O4, involving the Co3+/Co2+ cycle and oxygen vacancy formation at higher temperatures and likely the Langmuir¿Hinshelwood mechanism at lower temperature. Moreover, the results point to additional reaction pathways such as: 1) carbonate formation followed by decomposition; 2) CO dissociation followed by elementary carbon reoxidation in the overall CO oxidation reaction mechanism on Co3O4. An effect of the particle size of CoO materials on the catalytic activity was revealed. For CoO with particles of 20-50 nm, reoxidation of CoO to Co3O4 during CO oxidation (surface and near-surface) at 200 oC was monitored. In contrast, for macroscopic CoO (1 m) no bulk oxidation of CoO to Co3O4 was observed during CO oxidation at temperatures as high as 360 oC. Preferential CO oxidation on Co3O4 and CeO2-Co3O4 catalysts was studied third. The Co3O4 catalyst oxidation state during the PROX reaction was examined while simultaneously monitoring catalytic activity. Apart from the reaction mixture (CO, O2, H2), Co3O4 reduction in pure CO or H2 atmospheres were additionally examined. During PROX on Co3O4 the catalyst appears fully oxidized (i.e., both the surface and bulk oxidation state do not change up to 250 C). However, as revealed by reference measurements in (pure) CO, CO reduces the catalyst (surface) starting around 100 C via reaction with lattice oxygen. However, the reoxidation by O2 during PROX is fast enough to prevent overall reduction. Despite a very low concentration of oxygen vacancies under steady state PROX conditions, it is suggested that selective oxidation of CO to CO2 in an excess of H2 follows predominantly the Mars-van-Krevelen mechanism, referring to the information obtained from CO-O2 switching experiments. In (pure) H2, surface and bulk reduction both start above 250 C. Whilst the Co3O4 reduction to CoO and Co around 250 C explains the selectivity change to methanation, the change in selectivity around 170 C from PROX (with predominantly CO oxidation) to both CO and H2 oxidation cannot be explained by a change in (surface) oxidation state. Upon increasing the temperature the difference in the increase of H2 oxidation rate vs CO oxidation rate (higher apparent activation energy for H2 oxidation), as well as the competition for the limited amount of O2, are responsible for the decreasing CO oxidation selectivity. Furthermore, the effect of adding CeO2 (a less active material) to Co3O4 was studied. Promotion of Co3O4 with 10 wt% CeO2 increased the reduction temperatures in CO and H2 and enhanced the PROX activity. Since CeO2 is a less active material, this can only be explained by a higher activity of Co-O-Ce ensembles.