  One of the main objectives of the high-energy spin physics program at RHIC at
BNL is the precise determination of the polarized gluon distribution function,
$\Delta g(x)$. Polarized $\vec{p}+\vec{p}$ collisions at $\sqrt{s}=200\,$GeV
and at $\sqrt{s}=500\,$GeV at RHIC provide an unique way to probe the proton
spin structure. Inclusive measurements, such as inclusive jet and hadron
production, have so far been the prime focus of various results at
$\sqrt{s}=200\,$GeV constraining $\Delta g(x)$ for $0.05<x<0.2$. A recent
global analysis provides for the first time evidence of a non-zero value of the
gluon polarization $\int_{\tiny 0.05}^{\tiny 1}\Delta g (x)\, dx
\,(Q^{2}=10\,{\rm GeV}^{2}) = 0.20^{+0.06}_{-0.07}$. First results of di-jet
production at $\sqrt{s}=200\,$GeV by the STAR collaboration will allow a better
constraint of the underlying event kinematics. Extending the current program to
smaller values of $x$ is a key goal for the future high-energy spin physics
program at RHIC. Forward di-jet production measurements at STAR beyond the
current acceptance from $-1<\eta<+2$ to $+2.5<\eta<+4$, in particular those
carried out at $\sqrt{s}=500\,$GeV, provides access to low $x$ values at the
level of $10^{-3}$ where current uncertainties of $\Delta g(x)$ remain very
large. Those measurements will eventually be complemented by a future
Electron-Ion Collider facility probing $\Delta g(x)$ in polarized
$\vec{e}+\vec{p}$ collisions.
