Using the world's largest $e^+e^-$ collision data samples taken at
$\sqrt{s}=3.773$ GeV and $\sqrt{s}=4.178$ GeV with the integrated luminosities 2.93 fb$^{-1}$ and 3.19 fb$^{-1}$
accumulated by the BESIII detector at the Beijing Electron Positron Collider, precise measurements of the branching
fractions of $D \to K\mu^+\nu_\mu$, $D\to \pi\mu^+\nu_\mu$ and $D_{(s)}^+\to \mu^{+}\nu_{\mu}$ are reported. Combining the known branching fractions of $D\to \bar K e \nu_e$,
$D\to \pi e \nu_e$ and $D_{(s)}^+\to\tau^+\nu_\tau$, we have tested the lepton flavor universality with $D\to\bar K\ell^+\nu_\ell$, $D\to\pi\ell^+\nu_\ell$ and $D_{(s)}^+\to\ell^+\nu_\ell$ decays. We also determine the CKM matrix element $|V_{cs(d)}|$, the form factors $f_+^{D\to K(\pi)}(0)$ and $f_+^{D\to \eta'(\eta)}(0)$ of semileptonic $D$ decays, and the $D_{(s)}^+$ decay constant $f_{D_{(s)}^+}$ with the most precise accuracies to date.
Furthermore, searches for semileptonic $D$ decays to scalar and axial-vector mesons are also performed,
and these studies help us understand the internal structure of light mesons.