  We consider the transverse momentum dependent gluon distribution functions
(called gluon TMDs) by studying the light-front gluon-gluon correlator,
extending the results for unpolarized and vector polarized targets to also
include tensor polarized targets -- the latter type of polarization is relevant
for targets of spin $\ge1$. The light-front correlator includes
process-dependent gauge links to guarantee color gauge invariance. As from the
experimental side the gluon TMDs are largely unknown, we present positivity
bounds for combinations of leading-twist gluon distributions that may be used
to estimate their maximal contribution to observables. Since the gluonic
content of hadrons is particularly relevant in the small-$x$ kinematic region,
we also study these bounds in the small-$x$ limit for the dipole-type gauge
link structure using matrix elements of a single Wilson loop.
