  A high-energy Electron-Ion Collider (EIC) would offer a most promising tool
to study in detail the transverse momentum distributions of gluons inside
hadrons. This applies to unpolarized as well as linearly polarized gluons
inside unpolarized protons, and to left-right asymmetric distributions of
gluons inside transversely polarized protons, the so-called gluon Sivers
effect. The inherent process dependence of these distributions can be studied
by comparing to similar, but often complementary observables at LHC.
