Topological structure is one of the key techniques of flexible HVDC, which has great influence on the performance and cost of a project. The development status of flexible HVDC projects at home and abroad are introduced and the technological principle of VSC and MMC are analyzed. Then the current research on main electrical connection topological structure of flexible HVDC system are introduced, and their application range, advantages and disadvantages, etc. are concluded and analyzed. On the basis, the suggestion about taking flexible HVDC simulation technology as the interesting direction of next research is presented. This paper provides a theoretical reference for the topological structure research of flexible HVDC system in future.