First direct measurements of the weak decay constant fDs(fD)fDs(fD) and the Ds(D)Ds(D) branching fractions to μνμμνμ, ϕπϕπ, eXeX, ϕX(μνμ)ϕX(μνμ) at the BES experiments in 1990s are reviewed. Referring to the BESIII results of fDsfDs and branching fraction Br(Ds→μνμ)Br(Ds→μνμ) with best precision1 to date, prospect for challenge on precision measurements of fDsfDs and Br(Ds→μνμ)Br(Ds→μνμ) at BESIII is presented.