  Let $n\ge2$ and $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In
this article, the authors investigate global (weighted) estimates for the
gradient of solutions to Robin boundary value problems of second order elliptic
equations of divergence form with real-valued, bounded, measurable coefficients
in $\Omega$. More precisely, let $p\in(n/(n-1),\infty)$. Using a real-variable
argument, the authors obtain two necessary and sufficient conditions for
$W^{1,p}$ estimates of solutions to Robin boundary value problems,
respectively, in terms of a weak reverse H\"older inequality with exponent $p$
or weighted $W^{1,q}$ estimates of solutions with $q\in(n/(n-1),p]$ and some
Muckenhoupt weights. As applications, the authors establish some global
regularity estimates for solutions to Robin boundary value problems of second
order elliptic equations of divergence form with small $\mathrm{BMO}$
coefficients, respectively, on bounded Lipschitz domains, $C^1$ domains or
(semi-)convex domains, in the scale of weighted Lebesgue spaces, via some quite
subtle approach which is different from the existing ones and, even when $n=3$
in case of bounded $C^1$ domains, also gives an alternative correct proof of
some know result. By this and some technique from harmonic analysis, the
authors further obtain the global regularity estimates, respectively, in Morrey
spaces, (Musielak--)Orlicz spaces and variable Lebesgue spaces
