Abstract: A large amount of important astrophysical results has been achieved with Insight Hard X-ray Modulation Telescope (Insight-HXMT) since its launch in June 2017. So far Insight-HXMT has been operating smoothly in orbit and is expected to continue to operate in several more years. The purpose of this special issue is to allow a more comprehensive understanding by the Chinese astronomical community on the capability of Insight-HXMT, in order to continue to explore its scientific potential, especially in light of the fact that a series of domestic high-energy astrophysical missions have been launched recently or in development. The 11 papers cover most of the research progresses to date with Insight-HXMT.