  Recently, the charge radius of the proton was extracted for the first time
from muonic hydrogen. The value obtained is five standard deviations away from
similar measurements of regular hydrogen. This talk discusses work done in
collaboration with Richard J. Hill, to address this discrepancy. First, we have
studied the extraction of the charge radius of the proton from electron-proton
scattering data in a model-independent way. We have shown that previous
extractions, spanning a period of over 40 years, have underestimated their
errors. Second, we have looked at a model-independent analysis of proton
structure effects for hydrogen-like bound states, using the tool of an
effective field theory, namely NRQED. We have identified hidden model-dependent
assumptions in the theoretical calculation behind the muonic hydrogen result.
