The light pseudoscalar mesons $\eta$ and $\eta'$ are central to our understanding of QCD at low energies, and their decays provide important tests of effective field theories. They are also important laboratories for tests of discrete symmetries and searches for beyond Standard model physics. Through its large dataset at the $J/\psi$ resonance, the BESIII experiment has a unique opportunity to study the $\eta'$ meson and measure its decays with unprecedented precision. Recently, the absolute branching fractions of the five most common decay modes have been determined for the first time, and the rare decays $\eta'\to \pi^+\pi^-e^+e^-, \pi^+\pi^-\mu^+\mu^-, 4\pi^0,$ and $\gamma \gamma \eta$ have been studied with high precision.