Recent Progress in Leptonic and Semileptonic Decays of Charmed Hadrons

We present a comprehensive review of purely leptonic and semileptonic decays of $D^{0(+)}$, $D_s^{+}$, and charmed baryons (including $Λ_c^{+}$, $Ξ_c$ and $Ω_c$). 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 $Λ_c^{+}\barΛ_c^{-}$ offer important opportunities for studies of charm physics.