$D$ 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 $|V_{cs(d)}|$, 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.