  In November 2018, the CEPC released the Conceptual Design Report (CDR) with
the physics potential investigation and the analysis about different detector
concepts. Since then, intensive researches on the Higgs Physics at the CEPC
have been progressed. The run at top thresholds are also taken into
consideration and the physics potential around the center-of-mass energy of
360GeV is studied. The $ttH$ channel information boost the precision of Higgs
width measurement by a factor of 2 with respect to 240 GeV Higgs Runs.
Different Higgs decay modes are analyzed in the CEPC Higgs factory at the
center-of-mass energy of 240GeV, including Higgs to b/c/g and Higgs to
$\tau\tau$, which improves the Higgs measurement. Advanced analysis
technologies are developed and applied in the analysis, such as jet
reconstruction and lepton identification in jets. New interpretations are under
developing to improve the performance.
