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We review the progress on experimental studies of the non-$D\\bar D$ decays of the $\\psi(3770)$ resonance. With the world average of the observed cross sections for $D\\bar D$ production measured at 3.773 GeV by the MARK-I, MARK-II, BES and CLEO Collaborations, combined together with the cross section for $\\psi(3770)$ production at its peak as well as initial state radiative correction factor, we find that the non-$D\\bar D$ branching fraction of $\\psi(3770)$ decays is $B[\\psi(3770)\\to {\\rm non}-D\\bar D]=(19.8\\pm 1.8 \\pm 5.6)%$, which is consistent within error with $B[\\psi(3770)\\to {\\rm non}-D\\bar D]=(14.7\\pm 3.2)%$ measured previously by the BES Collaboration. In addition, a global amplitude analysis of the cross sections for $e^+e^- \\to {\\rm LH}$ (LH= light hadron) measured by the CLEO Collaboration shows that the light hadron branching fraction of $\\psi(3770)$ decays can be as large as about 11%. Combing the totally measured hadronic and ...