  We present a comprehensive review of purely leptonic and semileptonic decays
of $D^{0(+)}$, $D_s^{+}$, and charmed baryons (including $\Lambda_c^{+}$,
$\Xi_c$ and $\Omega_c$). The precise studies of these decays help deepen our
understanding and knowledge of quantum chromodynamics via measuring decay
constants and form factors, and test the Standard Model through examining the
unitarity of Cabibbo-Kobayashi-Maskawa matrix and lepton flavor universality.
We give an overview of the theoretical and experimental tools before discussing
the recent progress. The data sets collected by BESIII near the production
thresholds of $D\bar{D}$, $D_s^{(*)+}D_s^{(*)-}$ and
$\Lambda_c^{+}\bar{\Lambda}_c^{-}$ offer important opportunities for studies of
charm physics.
