QED by itself cannot perfectly describe simple atoms such as ordinary
or muonic hydrogen, because at a certain stage we need an adequate
description of the nuclear properties as input data.
Value of the proton radius is a key input parameter for the Lamb shift
in ordinary and muonic hydrogen. One can use its value to check QED,
or use QED to extract a value of the proton radius.
At present, there are three methods to determine the proton radius.
One is based on the elastic electron-proton scattering, while two
others are from spectroscopy of ordinary and muonic hydrogen. Present
days, the muonic value strongly disagrees with the ordinary-hydrogen
one and with the scattering one.
I will review the situation with determination of the proton radius,
mainly focusing in spectroscopic determinations.