Sulphoaluminate cement has excellent performances, such as low sintering temperature, low CO2 emission, fast hardening and early strength, frost resistance and impermeability. It has broad application prospects in the field of building materials and solid waste, and derived a series of sulphoaluminate cements such as belite-calcium sulphoaluminate cement and belite-barium calcium sulphoaluminate cement, and etc. However, belite (β-C2S), one of the main mineral components of above sulphoaluminate cement, has low hydration activity and slow hydration speed, easily resulting in slow growth of cement strength in the later stage. Ternesite (C5S2) was once considered to be an “inert” mineral, but it can show stronger hydration activity than β-C2S in sulphoaluminate system, so the research on ternesite-sulphoaluminate cement (TSAC) is of great significance. Firstly, this paper summarizes the research status of C5S2 and TSAC from aspects such as the formation and hydration of C5S2, and the preparation and performance of TSAC. Secondly, this paper puts forward the problems that TSAC needs to further study and solve, such as the exploration of solid waste materials, the performance regulation of TSAC and the optimization of mineral composition of TSAC clinker. Overall, it is expected to provide positive and favorable reference and support for the research and application of new low-carbon cement.