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 GeV, respectively. In addition, data sample with a luminosity of about 3 fb^(-1) at center-of-mass energies between 4.19 and 4.23 GeV are used to study D_s decays in some analyses. We report recent measurements that include the decays D_((s))^+→l^+ ν (l=μ,τ), D^0→K^- μ^+ ν_μ, D^+→η⁄(ωμ^+ ν_μ,) D^0(+) →ππe^+ ν_e, D^+→K_1 (1270)^0 e^+ ν_e, D_s^+→η^((')) e^+ ν_e and D_s^+→K^((*)) e^+ ν_e. From these analyses, the decay constants f_(D_((s)) ), the semileptonic form factors f_+^P (0) (P=K, η^((')), the CKM matrix elements |V_(cd(s)) | are determined precisely. These results can verify the LQCD calculations of f_(D_((s)) ), f_+^P (0) and the CKM matrix unitarity. Precision tests of lepton-flavor universality are also made via these decays.