The proton radius puzzle comes about from the discrepancy between measurements for the proton radius using electrons and using muons. The current CODATA data for only electronic spectroscopy data is 0.8758(77) fm . Including electron scattering results, CODATA finds the overall result of 0.8775(51) fm. The first results of muonic hydrogen (Collaboration of Randolf Pohl et al.) based on the 2S-2P Lamb shift energy splitting yields 0.84087(39) fm for the proton radius. This is 4% smaller than the CODATA radius, and is a 7σ discrepancy. The latest results of the same collaboration confirms this result. Why is there this discrepancy?
The discrepancy comes from the fact that, as muonic hydrogen has a very short radius, it is more sensitive to the true electric charge distribution which, on the other hand, cannot be explained by three pointlike quarks, as shown in the post The article PLOT OF THE WEEK – QUARK COMPOSITENESS IS NOWHERE NEAR is wrong in this web page. Therefore, the above mentioned discrepancy has to do with quark compositeness.
For a broad account of the proton radius puzzle, please take a look at the paper by Carl E. Carlson The Proton Radius Puzzle. For the latest theoretical developments, please take a look at the work of the TRIUMF group.