Abstract Quarkonia states are expected to provide essential information on the properties of the high-density strongly-interacting system formed in the early stages of high-energy heavy-ion collisions. ALICE is the LHC experiment dedicated to the study of nucleus-nucleus collisions and can study charmonia at forward rapidity (2.5<y<4) via the μ+μ− decay channel and at mid rapidity (|y|<0.9) via the e+e− decay channel. In both cases charmonia are measured down to zero transverse momentum. The inclusive J/ψ production as a function of transverse momentum and rapidity in pp collisions at s=7TeV, the inclusive J/ψ production as a function of the charged particle multiplicity, the inclusive J/ψ polarization at forward rapidity and the J/ψ prompt to non-prompt fraction are discussed. Finally, the analysis of the inclusive J/ψ production in the Pb–Pb data collected fall 2011 at a center of mass energy of sNN=2.76TeV is presented. Results on the nuclear modification factor are then shown as a function of centrality, transverse momentum and rapidity and compared to model predictions. First results on inclusive J/ψ elliptic flow are given.