  Linear polarization of gluons inside unpolarized hadrons affects the
transverse momentum distribution of produced spin-0 particles, such as of the
Higgs or (pseudo-)scalar quarkonium states at LHC. Despite the currently
unknown amount of linear gluon polarization, a range of predictions can be
obtained, using TMD evolution, which indicates that their effect is on the few
percent level in Higgs production, but can be much larger in quarkonium
production. Together with asymmetries in open charm or bottom production in
electro-production at an Electron-Ion Collider, the size and sign of the linear
gluon polarization could be extracted experimentally. These processes also
allow to test the behavior expected at small $x$ in and outside the saturation
region.
