Materials characterisation plays a crucial role in developing thermal barrier coatings and environmental barrier coatings for gas-turbine engines. The failure of thermal barrier coatings and environmental barrier coatings is influenced by a complex interdependence of microstructure, residual stress, and thermomechanical properties. Validating our mechanistic understanding of each of these factors that contribute to failure requires a selection of suitable characterisation techniques. Presented in this review are characterisation techniques, both ex situ and in situ, that have advanced the understanding of thermal barrier coating and environmental barrier coating failure. Targeted coating development that is both effective and efficient depends on these characterisation techniques to obtain superior coatings with improved performance and lifetime.