Abstract: In recent years, various large space structures are gradually implemented in the aerospace industry of China. Thus, the corresponding thermally induced vibration problems are drawn more and more attentions. Under this background, it is necessary to clarify the underling mechanism of the thermally induced vibration phenomenon and the corresponding critical issues in the analysis and design. Based on the research work of the authors, this article gives a comprehensive review of the related problems and mainly focuses on some special aspects in the thermally induced vibration analysis of complex engineering structures, which are compose of many thin-walled bars. Firstly, this article introduces a Fourier finite element that decomposes the temperature into the average part and the perturbation part. In this way, the thermal conduction equation under thermal radiation can be decoupled into the corresponding two parts due to the orthogonal property of the Fourier series. Thus, the transient temperature field of closed-section or open-section thin-walled bars can be efficiently analyzed. Based on this kind of element, both linear and nonlinear methods for the thermally induced vibration analysis are presented with the emphasis on the thermal-dynamic coupling effect. In order to give the analytical form of the necessary condition of the thermally induced vibration, this paper analyzes the properties of the transient temperature and the oscillation displacement in the mode space, and thus it obtains a general criterion to evaluate the intensity of the thermally induced vibration. Based on these work, the dynamic stability of the thermally induced vibration is further discussed by not only the mechanism reflected in the thermal flutter criterion of a cantilever bar, but also the thermal flutter analysis of complex engineering structures. Finally, the conclusion part briefly addresses some important factors in the underground testing and the method of suppressing the thermally induced responses. Some research topics need further investigating in the future are also envisaged.