Thermal barrier coatings (TBCs) are crucial for increasing the turbine inlet temperature (and hence efficiency) of gas turbine engines. The thesis describes PhD research aimed at improving understanding of the thermal cycling failure mechanisms of electron beam physical vapour deposited (EB-PVD) yttria stabilised zirconia (YSZ) TBCs on single crystal superalloys. The research consisted of three different stages. The first stage involved designing a coupled one-dimensional thermodynamic-kinetic oxidation and diffusion model capable of predicting the concentration profiles of alloying elements in a single-phase γ nickel-rich Ni-Al-Cr ternary alloy by the finite difference method. The aim of this investigation was to improve the understanding of interactions between alloying species and developing oxide. The model demonstrated that in the early stages of oxidation, Al consumption by oxide scale growth is faster than Al replenishment by diffusion towards the scale, resulting in an initial Al depletion in the alloy near the scale. The second stage involved a systematic study of the life-time of TBC systems on different single crystal superalloys. The study aimed at demonstrating that the compatibility of modern nickel-based single crystal superalloys with TBC systems is influenced strongly by the content of alloying element additions in the superalloy substrate. The results can be explained by postulating that the fracture toughness parameters controlling decohesion are influenced strongly by small changes in composition arising from interdiffusion with the bond coat, which itself inherits elemental changes from the substrate. The final stage of study involved a detailed study of different bond coats (two β-structured Pt-Al types and a γ/γ’ Pt-diffusion type) in TBC systems based on an EB-PVD YSZ top coat and a substrate material of CMSX-4 superalloy. Generation of stress in the thermally grown oxide (TGO) on thermal cycling, and its relief by plastic deformation and fracture, were investigated experimentally in detail.