  The rms-radius $R$ of the proton charge distribution is a fundamental
quantity needed for precision physics. This radius, traditionally determined
from elastic electron-proton scattering via the slope of the Sachs form factor
$G_e(q^2)$ extrapolated to momentum transfer $q^2$=0, shows a large scatter. We
discuss the approaches used to analyze the e-p data, partly redo these analyses
in order to identify the sources of the discrepancies, and explore alternative
parameterizations. The problem lies in the model dependence of the
parameterized $G(q)$ needed for the extrapolation. This shape of $G(q<q_{min})$
is closely related to the shape of the charge density $\rho (r)$ at large radii
$r$, a quantity which is ignored in most analyses. When using our {\em physics}
knowledge about this large-$r$ density together with the information contained
in the high-$q$ data, the model dependence of the extrapolation is reduced and
different parameterizations of the pre-2010 data yield a consistent value for
$R = 0.887 \pm 0.012fm$. This value disagrees with the more precise value
$0.8409 \pm 0.0004 fm$ determined from the Lamb shift in muonic hydrogen.
