  Charmonia with different transverse momentum $p_T$ usually comes from
different mechanisms in the relativistic heavy ion collisions. This work tries
to review the theoretical studies on quarkonium evolutions in the deconfined
medium produced in p-Pb and Pb-Pb collisions. The charmonia with high $p_T$ are
mainly from the initial hadronic collisions, and therefore sensitive to the
initial energy density of the bulk medium. For those charmonia within
$0.1<p_T<5$ GeV/c at the energies of Large Hadron Collisions (LHC), They are
mainly produced by the recombination of charm and anti-charm quarks in the
medium. In the extremely low $p_T\sim 1/R_A$ ($R_A$ is the nuclear radius),
additional contribution from the coherent interactions between electromagnetic
fields generated by one nucleus and the target nucleus plays a non-negligible
role in the $J/\psi$ production even in semi-central Pb-Pb collisions.
