  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.
