  A comprehensive review of weak decays of charmed hadrons ($D^{0/+}$, $D^+_s$
and $\Lambda^+_c$) based on analyses of the threshold data from $e^+e^-$
annihilation in the BESIII experiment is presented. Current experimental
challenges and successes in understanding decays of the charmed hadrons are
discussed. Precise calibrations of QCD and tests of the Standard Model are
provided by measurements of purely leptonic and semi-leptonic decays of charmed
hadrons, and lepton universality is probed in purely leptonic decays of charmed
mesons to three generations of leptons. Quantum correlations in threshold data
samples provide access to strong phases in the neutral $D$ meson decays and
probe the decay dynamics of the charmed $\Lambda_c$ baryon. Charm physics
studies with near-threshold production of charmed particle pairs are unique to
BESIII, and provide many important opportunities and challenges.
