Hundreds of different types of coatings are used to protect a variety of structural engineering materials from corrosion, wear, and erosion, and to provide lubrication and thermal insulation. Of all these, thermal barrier coatings (TBCs) have the most complex structure and must operate in the most demanding high-temperature environment of aircraft and industrial gas-turbine engines. TBCs, which comprise metal and ceramic multilayers, insulate turbine and combustor engine components from the hot gas stream, and improve the durability and energy efficiency of these engines. Improvements in TBCs will require a better understanding of the complex changes in their structure and properties that occur under operating conditions that lead to their failure. The structure, properties, and failure mechanisms of TBCs are herein reviewed, together with a discussion of current limitations and future opportunities.