  We explain a gluon transversity, transverse-momentum-dependent parton
distribution functions (TMDs), and parton distribution functions (PDFs) for
spin-1 hadrons. The gluon transversity exists in hadrons with spin more than or
equal to one, and it does not exist in the spin-1/2 nucleons. Since there is no
direct contribution from the nucleons, it is an appropriate quantity to probe
an exotic component in the spin-1 deuteron beyond a simple bound system of the
nucleons. We show how the gluon transversity can be measured at hadron
accelerator facilities by the Drell-Yan process in addition to
lepton-accelerator experiments. Next, possible TMDs are explained for the
spin-1 hadrons at the twists 3 and 4 in addition to twist-2 ones by considering
tensor polarizations. We found that 30 TMDs exist in the tensor-polarized
spin-1 hadron at the twists 3 and 4 in addition to 10 TMDs at the twist 2.
There are 3 collinear PDFs at the twists 3 and 4. We also indicate that the
corresponding TMD fragmentation functions exist at the twists 3 and 4. Due to
the time-reversal invariance in the collinear PDFs, there are new sum rules on
the time-reversal odd TMDs. In addition, we obtained a useful twist-2 relation,
a sum rule, and relations with multiparton distribution functions by using the
operator product expansion and the equation of motion for quarks. These
findings are valuable for experimental investigations on polarized deuteron
structure functions in 2020's and 2030's at world accelerator facilities.
