As a third-generation semiconductor material, silicon carbide (SiC) has excellent properties such as wide bandgap, high thermal conductivity, high saturation electron drift velocity, strong radiation resistance, good thermal and chemical stability, et al. It has great application potential in high temperature, high power, high frequency power electronic devices and radio frequency devices. The production of high-quality, large-size, and low-cost SiC single crystal substrates is a prerequisite for large-scale applications of SiC devices. However, the supply of SiC single crystal substrates still faces some challenges, such as high defect density, low yield and high cost. High temperature solution growth (HTSG) technique, with top seeded solution growth (TSSG) as the main technical model at present, has advantages of fabrication of SiC with low defects density, easy to enlarge diameter, and easy to obtain p-type doping. In the future, it is expected to become one of the mainstream technologies to mass produce SiC single crystals. In this paper, the development of SiC single crystal grown by TSSG is reviewed firstly. Then the principle and growth process of SiC single crystal growth by TSSG are introduced and analyzed. The research progress of TSSG for SiC single crystal growth is summarized from crystal growth thermodynamics and kinetics. The unique advantages of this technology are summarized. Finally, the future research direction and challenges of this method are given.