  We report on published charmonium measurements performed by ALICE, at the
LHC, in Pb-Pb collisions at a center of mass energy per nucleon-nucleon
collision $\sqrt{s_{\rm NN}} = 2.76$ TeV, at both mid ($|y|<0.8$) and forward
($2.5<y<4$) rapidities. The nuclear modification factor of inclusive ${\rm
J}/\psi$ is presented as a function of the collision centrality and the ${\rm
J}/\psi$ transverse momentum, $p_{\rm T}$. The variation of the ${\rm J}/\psi$
mean transverse momentum square as a function of the collision centrality is
also discussed. These measurements are compared to state of the art models that
include one or several of the following mechanisms: color screening of the
charm quarks, statistical hadronization at the QGP phase boundary, balance
between ${\rm J}/\psi$ dissociation and regeneration in the QGP, ${\rm J}/\psi$
interaction with a dense comoving medium. Results on the production of the
heavier and less bound $\psi'$ meson in Pb-Pb collisions at forward-rapidity
are also presented and compared to both models and measurements performed by
other experiments. At mid-rapidity we also report on ALICE unique capability to
separate prompt and non-prompt ${\rm J}/\psi$ production down to low $p_{\rm
T}$ ($\geq 1.5$ GeV/$c$) and thus disentangle between effects on prompt ${\rm
J}/\psi$ mesons and energy loss of $b$ quarks in the QGP.
