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We explain spin structure for a spin-one hadron, in which there are newstructure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) whichexist for the spin-1/2 nucleon, associated with its tensor structure. The newstructure functions are $b_1$, $b_2$, $b_3$, and $b_4$ in deep inelasticscattering 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 structurefunctions are introduced, and useful formulae are derived for projectionoperators of $b_{1-4}$ from a hadron tensor $W_{\mu\nu}$. Second, a sum rule isexplained for $b_1$, and possible tensor-polarized distributions are discussedby using HERMES data in order to propose future experimental measurements andto compare them with theoretical models. A proposal was approved to measure$b_1$ at the Thomas Jefferson National Accelerator Facility (JLab), so thatmuch progress is expected for $b_1$ in the near future. Third, formalisms ofpolarized proton-deuteron Drell-Yan processes are explained for probingespecially tensor-polarized antiquark distributions, which were suggested bythe HERMES data. The studies of the tensor-polarized structure functions willopen a new era in 2020's for tensor-structure studies in terms of quark andgluon degrees of freedom, which is much different from ordinary descriptions interms of nucleons and mesons.

Tensor-polarized structure functions: Tensor structure of deuteron in 2020's