  I discuss Upsilon production in pp collisions at RHIC, Tevatron and LHC
energies, in particular the behaviour of the differential cross section in
rapidity and the impact of QCD corrections on the P_T differential cross
section. I also emphasise the very good agreement between the parameter-free
predictions of the Colour-Singlet Model (CSM) and the first LHC data,
especially in the region of low transverse momenta, which is the most relevant
one for heavy-ion studies. I also show that the CSM predicts Upsilon
cross-section ratios in agreement with the most recent LHC data. I then briefly
discuss the nuclear-matter effects on Upsilon production at RHIC and the LHC in
p(d)A collisions and, by extension, in AA collisions. I argue that a) the
Upsilon break-up probability can be neglected, at RHIC and the LHC, b) gluon
shadowing --although non-negligible-- is not strong enough to describe forward
RHIC data, c) backward RHIC data hints at a gluon EMC effect, possibly stronger
than the quark one. Outlooks for the LHC pPb run are also presented.
