  We explain spin structure for a spin-one hadron, in which there are new
structure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) which
exist for the spin-1/2 nucleon, associated with its tensor structure. The new
structure functions are $b_1$, $b_2$, $b_3$, and $b_4$ in deep inelastic
scattering of a charged-lepton from a spin-one hadron such as the deuteron.
Among them, twist-two functions are related by the Callan-Gross type relation
$b_2 = 2 x b_1$ in the Bjorken scaling limit. First, these new structure
functions are introduced, and useful formulae are derived for projection
operators of $b_{1-4}$ from a hadron tensor $W_{\mu\nu}$. Second, a sum rule is
explained for $b_1$, and possible tensor-polarized distributions are discussed
by using HERMES data in order to propose future experimental measurements and
to compare them with theoretical models. A proposal was approved to measure
$b_1$ at the Thomas Jefferson National Accelerator Facility (JLab), so that
much progress is expected for $b_1$ in the near future. Third, formalisms of
polarized proton-deuteron Drell-Yan processes are explained for probing
especially tensor-polarized antiquark distributions, which were suggested by
the HERMES data. The studies of the tensor-polarized structure functions will
open a new era in 2020's for tensor-structure studies in terms of quark and
gluon degrees of freedom, which is much different from ordinary descriptions in
terms of nucleons and mesons.
