Solid oxide fuel cell (SOFC) is a high-efficiency, fuel-flexible, all-solid-state fuel cell, which is the focus of competing research and development around the world. It operates at a high temperature for a long time, and the material properties of the running components are quite different. The problems of component damage and failure caused by the inevitable internal thermal stress severely affect its commercial application. The thermal failure of SOFC has different manifestations and mechanisms in different scales. This review summarized recent work on the stack, single cell and electrode. The corresponding comments and suggestions in this field were given. This review could provide a guidance for studies on the thermal failure problems of SOFCs.