In modern gas-turbine engines, thermal barrier coatings (TBCs) are used to provide thermal protection for the underlying metallic components. In this thesis, 3D X-ray micro-computed tomography (μ-CT) has been applied to characterise TBCs, with an attempt to non-destructively track their microstructure degradation and correlate their thermal conductivity with their microstructural details.TBCs deposited via electron-beam physical vapour deposition (EB-PVD) with a β-Ni(Pt)Al bond coat have been widely used in high-pressure turbine blades for aeroengines. Using destructive characterisation techniques, it has been found that multiple degradation processes occur simultaneously during thermal cycling. However, no direct tracking of the degradation during thermal cycling at the same sample position has been reported. Therefore, the microstructure degradation process of an EB-PVD TBC with a β-Ni(Pt)Al bond coat during thermal cycling at 1150 °C was followed non-destructively using X-ray μ-CT. The feasibility of X-ray μ-CT is validated by cross-sectional SEM micrographs of a reference sample subjected to the same thermal cycling test. X-ray μ-CT results are in accordance with the predictions from the TGO growth mechanisms and the ratcheting mechanism for TGO undulation evolution.The thermal conductivity of an air-plasma sprayed (APS) TBC is studied. Meanwhile, microstructurally realistic models are developed from μ-CT virtual slices of the same sample. It is found that inter-splat cracks and interfaces can significantly reduce the thermal conductivity of the coating. Sintering at 1100 °C for 10 h leads to a thermal conductivity comparable to the predictions from image-based models. This suggests that in the long run, the effective thermal conductivity is determined by the pores revealed by X-ray μ-CT. The shape of the pores is found to be dependent on their volume. The larger the pore, the higher its aspect ratio is. In addition, the larger pores are more preferentially aligned to the coating's spray direction. As a result, the volume averaged thermal conductivity reduction is higher for pores with a bigger volume.As a potential candidate to the self-healing TBC material, the fracture toughness of an YSZ ceramic embedded with 20 vol. % MoSi2 prepared by sparking plasma sintering (SPS) is studied. Four-point bending test and digital image correlation (DIC) give comparable fracture toughness values of ~ 2 MPa√m. The crack/particle interaction is revealed by DIC. It is found that the crack tends to cut through the particle/matrix interface. Defects (i.e. pores) at the interface is found. In addition, the residual stress induced by the misfit in thermal expansion coefficients leads to a local tensile hoop stress around the particle. These two factors are responsible for the predominant interfacial cracking.