We present a comprehensive review of purely leptonic and semileptonic decays of D0(+), [Formula: see text], and charmed baryons (including [Formula: see text], 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 the 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 the Beijing Spectrometer III (BESIII) near the production thresholds of [Formula: see text], [Formula: see text], and [Formula: see text] offer important opportunities for studies of charm physics.