  Many new physics models beyond the Standard Model, motivated by the recent
astrophysical anomalies, include the possibility of several new types of light
weak-interacting particles. Typical models, such as Next-to-Minimal
Supersymmetric Standard Model and Hidden Dark-sector Model, predict the light
Higgs and dark bosons, respectively. The masses of these particles are expected
to be a few GeV and thus making them accessible at BESIII. BESIII has recently
explored the possibility of light Higgs and dark bosons in several decay modes
using the data-sets collected at $J/\psi$, $\psi(3686)$ and $\psi(3770)$
resonances. The $J/\psi$ data have further utilized to search for invisible
decays of light vector ($V=\omega, \phi$) and pseudo-scalar ($P=\eta, \eta'$)
mesons via $J/\psi \to VP$ decays. This report summarizes the recent results of
the BESIII experiment on these new physics topics.
