Carbon capture power plants（CCPPs） will endow future power industry with completely new operation mechanism and development prospects， and are showing great research significance. Carbon capture technology has drawn much attention. Most of the researches in this field， however， are focusing on the rated condition and static state of CCPPs， while only a small amount of literatures have considered the flexible operation of CCPPs. The potential， implementation and technical characteristics of the flexible operation of CCPPs are analyzed in the view of a single power plant and of the whole power system， respectively. The paper reveals the excellent performance of the flexible operation of CCPPs， indicating that the flexible operation of CCPPs will bring additional profits to power system. The paper presents the research emphases and development direction of the flexible operation of CCPPs in the future， trying to establish a research framework of the flexible operation of CCPPs， with the expectation to provide some analysis and thoughts for the researchers in this field.