  As an unstable light pure leptonic system, positronium is a very specific
probe atom to test bound state QED. In contrast to ordinary QED for free
leptons, the bound state QED theory is not so well understood and bound state
approaches deserve highly accurate tests. We present a brief overview of
precision studies of positronium paying special attention to uncertainties of
theory as well as comparison of theory and experiment. We also consider in
detail advantages and disadvantages of positronium tests compared to other QED
experiments.
