Photon structure function revisited

The flux of papers from electron positron colliders containing data on the photon structure function ended naturally around 2005. It is thus timely to review the theoretical basis and confront the predictions with a summary of the experimental results. The discussion will focus on the increase of the structure function with x (for x away from the boundaries) and its rise with log Q**2, both characteristics beeing dramatically different from hadronic structure functions. The agreement of the experimental observations with the theoretical calculations of the real and virtual photon structure is a striking success of QCD. It also allows a new determination of the QCD coupling constant which very well agrees with the value quoted in the literature.