Open and hidden heavy-flavor measurements with the ALICE experiment at the LHC are reported. Emphasis goes to the recent results in p–Pb and Pb–Pb collisions at sNN=5.02 and 2.76 TeV respectively. Heavy-flavor measurements are presented in the form of either the ratio of the production cross sections in heavy-ion and pp collisions normalized by the average number of nucleon-nucleon collisions, or the per-event yields as a function of charged-particle multiplicity. Possible interpretations of these results in pp, p–Pb or Pb–Pb collisions in terms of multi-parton interactions, gluon saturation, initial or final state energy loss, system collective motion, color-charge screening or recombination of uncorrelated quarks are discussed.