The present monograph deals with new advanced materials, including composites, functionally graded materials, materials for high temperature service, advanced approaches to local and non-local analysis of localized damage, new description of crack deactivation, and many more. It contains the following subjects: Survey of material properties for high temperature and other extreme conditions Thermodynamics of constitutive modelling of advanced materials Developing and implementing selected constitutive models for thermo-elasto-plastic-damage materials Developing and implementing constitutive models for the specific functionally graded materials, with special attention paid to thermal barrier coatings Methodology of experimental microstructure analysis and residual stress determination with application to several materials and components includig functionally graded materials.