Rare decays of charm hadrons and charmonium provide a powerful laboratory
for testing the Standard Model (SM) at the intensity frontier.
These processes are forbidden at tree level or strongly suppressed by the
Glashow--Iliopoulos--Maiani (GIM) mechanism, making them sensitive probes of
physics beyond the SM, including heavy virtual particles, Majorana neutrinos,
and interactions with a dark sector.
Using the world's largest data samples collected at the $\tau$--charm threshold
and more than $10^{10}$ $J/\psi$ events, the BESIII experiment has carried out
a comprehensive program of searches for flavor-changing neutral currents (FCNC),
lepton and baryon number violation, weak decays of the $J/\psi$ meson,
and invisible decays.
While no unambiguous signal of new physics has been observed,
several rare processes are studied for the first time and
the most stringent limits to date are established in multiple channels.