  The study of quarkonia in heavy-ion collisions has been the subject of
intense experimental and theoretical effort, ever since their production was
predicted to be sensitive to the formation of a deconfined state of
strongly-interacting matter, known as the Quark-Gluon Plasma (QGP). In p-Pb
collisions, Cold Nuclear Matter (CNM) effects, such as nuclear shadowing or
partonic energy loss, are expected to influence quarkonium production. The
study of such system is therefore crucial to shed light on the mechanisms
taking place at the initial-state of quarkonium production, and to disentangle
the cold and hot nuclear effects envisioned in Pb-Pb collisions. The ALICE
experiment at the LHC, is capable of reconstructing J/$\psi$, $\psi$(2S) and
$\Upsilon$ states at forward rapidity through their $\mu^{\rm{+}}\mu^{\rm{-}}$
decay channel, as well as J/$\psi$ at central rapidity through their
$e^{\rm{+}}e^{\rm{-}}$ decay channel, down to zero transverse momentum. A
review of the main ALICE findings from the measurements of the inclusive
quarkonium yields in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV,
collected during the LHC Run I period, as well as more recent results from
J/$\psi$ measurements in p-Pb at $\sqrt{s_{\rm{NN}}}$ = 8.16 TeV, from LHC Run
II period, will be presented in this paper.
