$D$ leptonic and semileptonic decays

Based on 2.92 fb${}^{-1}$ data taken at the center-of-mass energy $\sqrt s=3.773$ GeV with the BESIII detector, we report recent results on the decay constant $f_{D^{+}}$, the hadronic form factors, as well as the quark mixing matrix elements $\mathrm{\mid }{V}_{cs(d)}\mathrm{\mid }$, which are extracted from analyses of the leptonic decay $D^{+}\to {\mu }^{+}{\nu }_{\mu }$ and the semileptonic decays $D^0\to K(\pi)^-e^+\nu_e$,$D^+\to K^0_L e^+\nu_e$,$D^+\to K^-\pi^+e^+\nu_e$and$D^+\to \omega(\phi)e^+\nu_e$ at BESIII.