The world's largest sample of J/psi) events, 1.31 billion events accumulated at the BESIII detector, provides a unique opportunity to investigate eta and eta' physics via two-body J/psi radiative or hadronic decays. For many eta' decay channels the low background data samples are up to three orders of magnitude larger than collected in any previous experiment. Here we review the most significant results on eta and eta' obtained at BESIII so far. The analyses range from detailed studies of common decay dynamics, observations of new radiative and Dalitz decays, and searches for rare/forbidden decays with sensitivity up to B similar to 10(-5). Finally, prospects of forthcoming runs at the J/psi peak for eta and eta' physics are discussed.