The proton radius puzzle is the difference between the proton radius as measured with electron scattering and in the excitation spectrum of atomic hydrogen, and that measured with muonic hydrogen spectroscopy. Since the inception of the proton radius puzzle in 2010 by the measurement of Pohl et al.[1], many possible resolutions to the puzzle have been postulated, but, to date, none has been generally accepted. New data are therefore necessary to resolve the issue. We briefly review the puzzle, the proposed solutions, and the new electron scattering and spectroscopy experiments planned and underway. We then introduce the MUSE experiment, which seeks to resolve the puzzle by simultaneously measuring elastic electron and muon scattering on the proton, in both charge states, thereby providing new information to the puzzle. MUSE addresses issues of two-photon effects, lepton universality and, possibly, new physics, while providing simultaneous form factor, and therefore radius, measurements with both muons and electrons.