BESIII has collected data samples corresponding to luminosities of 2.93 fb-1 and 3.19 fb-1 at center-of-mass energies of 3.773 and 4.178, respectively. We report recent measurements that include the decays D(s)+ -> l+v (l=mu, tau), D0(+) -> K-bar(pi)l+v (l=e,mu), D0(+) -> a0(980)e+v, D+->K1(1270)e+nu, D(s)+ -> eta(')e+nu, Ds+ -> K(*0)enu, Ds+ -> phi enu,. The first searches for Ds+ -> gamma e+nu and Ds+ -> pp-bar e+nu are also presented. From these analyses, the decay constants fD(s)+, the semileptonic form factors f^P_+(0) [P=K, pi, eta(')], the CKM matrix elements |Vcs(d)| are determined precisely. These results can verity the LQCD calculations of fD(s)+ ,f^P_+(0) and the CKM matrix unitarity. Precision tests of lepton flavor universality are also made via D(s)+ -> l+v and D0(+) -> K-bar(pi)l+v, decays.