  Protons are bound states of the strong interaction governed by Quantum
Chromodynamics (QCD). Its charge radius ($r_{E}^{p}$) is an important quantity
as it characterizes the spatial distribution of the proton's charge, which is
carried by the quarks. On the other hand, the proton charge radius is an
essential physical input for the bound-state Quantum Electrodynamic (QED)
calculations for the hydrogen atomic energy levels. Nevertheless, the large
discrepancy between $r_{E}^{p}$ measurements from muonic hydrogen spectroscopy,
and those from $ep$ elastic scattering and ordinary hydrogen spectroscopy, have
been puzzling physicists for over a decade. Tremendous efforts, in both
theoretical and experimental sides, have been dedicated to providing various
insights into this puzzle, yet certain issues still remain unresolved,
particularly in the field of lepton scatterings. This review will focus on
$r_{E}^{p}$ measurements using lepton scatterings, the recent theoretical and
experimental developments in this field, as well as future experiments using
this technique.

Nuclear Experiment;High Energy Physics - Experiment;High Energy Physics - Phenomenology;Nuclear Theory