  The description of the polarized quark hadronization process is one of the
most challenging problems in the physics of strong interactions. The various
single hadron and dihadron fragmentation functions, that quantify this process,
are determined by analyzing the inclusive production of hadrons in
electron-positron semi-inclusive annihilation process (SIA). These, in turn,
are used to extract the transverse momentum dependent parton distribution
functions from the experiments on semi-inclusive deep inelastic scattering
process (SIDIS), elucidating the spin-orbit correlations in nucleon.
  Here we present a framework for new measurements of polarized quark
fragmentation functions in electron-positron annihilation and deep inelastic
semi-inclusive processes. These measurements offer a number of exciting
opportunities to improve our understanding of the polarized quark hadronization
and test the universality of the fragmentation functions. Such measurements can
be performed at the upcoming BELLE II, JLab-12 and the future EIC experiments
