Ceramic thermal and environmental barrier coatings (TEBCs) are used in gas turbine engines to protect engine hot-section components in the harsh combustion environments, and extend component lifetimes. Advanced TEBCs that have significantly lower thermal conductivity, better thermal stability and higher toughness than current coatings will be beneficial for future low emission and high performance propulsion engine systems. In this paper, ceramic coating design and testing considerations will be described for turbine engine high temperature and high-heat-flux applications. Thermal barrier coatings for metallic turbine airfoils and thermal/environmental barrier coatings for SiC/SiC ceramic matrix composite (CMC) components for future supersonic aircraft propulsion engines will be emphasized. Further coating capability and durability improvements for the engine hot-section component applications can be expected by utilizing advanced modeling and design tools.