  Polarization measurements are the best instrument to understand how quark and
antiquark combine into the different quarkonium states, but no model has so far
succeeded in explaining the measured J/psi and Upsilon polarizations. On the
other hand, the experimental data in proton-antiproton and proton-nucleus
collisions are inconsistent, incomplete and ambiguous. New analyses will have
to properly address often underestimated issues: the existence of azimuthal
anisotropies, the dependence on the reference frame, the influence of the
experimental acceptance on the comparison with other measurements and with
theory. Additionally, a recently developed frame-invariant formalism will
provide an alternative and often more immediate physical viewpoint and, at the
same time, will help probing systematic effects due to experimental biases. The
role of feed-down decays from heavier states, a crucial missing piece in the
current experimental knowledge, will have to be investigated. Ultimately,
quarkonium polarization measurements will also offer new possibilities in the
study of the properties of the quark-gluon plasma.
