The Advanced Space-based Solar Observatory (ASO-S) was formally approved at the end of 2017.In the past two years,ASO-S underwent its official Phase-B and Phase-C studies.The Phase-B study was successfully accomplished by the end of April 2019,and the Phase-C study is being now undertaken until August 2020.Then the flight model is planned to finish within 16 months.Around the end of 2021,ASO-S will be ready in the launch state.We briefly summarize the history of ASO-S,the phase-B studies,and the phase-C studies.