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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., Proceedings of DPF2011, Meeting of the Division of Particles and Fields of the American Physical Society, Brown University, Providence, Rhode Island, USA, August 8-13, 2011 and Proceedings of PANIC 2011, 19th Particles & Nuclei International Conference, MIT, Cambridge, Massachusetts, USA, July 24-29 2011, and eConf C110809 (2012)