  The STAR experiment has been studying the spin structure of the proton, using
the unique high-energy polarized proton collider, the Relativistic Heavy Ion
Collider (RHIC). The kinematic coverage at STAR allows accessing gluons because
quark-gluon and gluon-gluon scatterings dominate particle production at low and
medium transverse momenta. The polarized gluon distribution function can be
constrained by measuring the longitudinal double-spin asymmetry ($A_{LL}$) of
jet production and neutral pions. Global QCD analyses of polarized parton
distribution functions, which include the 2009 $A_{LL}$ STAR results for
inclusive jet production at $\sqrt{s}=200$ GeV, provide evidence of a non-zero
gluon polarization in the measured range of partonic momentum fraction $x >
0.05$. We present the status of the latest measurements of $A_{LL}$ at STAR,
for inclusive jet and dijet production at $\sqrt{s}=510$ GeV and 200 GeV
collected in 2013 and 2015 respectively, both at mid-rapidity ($|\eta|<0.9$).
The large data sample taken during these years will improve the precision of
our knowledge about the proton spin structure while the increased center of
mass energy allows probing the polarized gluon distribution function at smaller
partonic momentum fraction. Furthermore, we present measurements of $A_{LL}$
for neutral pions at forward rapidity ($2.65<\eta<3.9$) collected during 2012
and 2013 that also allow reaching lower partonic momentum fraction. We compare
these measurements with the latest global analyses.
