The suppression of charmonium states was also observed in proton-lead collisions at the LHC, in which Quark Gluon Plasma is not formed. This suggests that the observed suppression in proton-nucleus collisions (pA) is due to cold nuclear matter effects. Grasping the wealth of experimental results requires understanding the medium modification of quarkonia and disentangling hot and cold-matter effects. Today there is a large amount of data available from RHIC and LHC on charmonium and bottomonium suppression and ALICE tries to distinguish between effects due to the formation of the QGP and those from cold nuclear matter effects.