ALICE is the LHC experiment devoted to the study of heavy-ion collisions. While results from Pb-Pb collisions at √sNN = 2.76 TeV provide insight on the properties of the plasma of quarks and gluons, formed in nucleus-nucleus interactions, the study of p-Pb collisions at √sNN = 5.02 TeV allows a deeper understanding of cold nuclear matter effects. Therefore, p-Pb results turn out to be a powerful tool to provide a baseline for Pb-Pb, to correctly quantify how the various observables are affected by genuine hot medium effects. In this proceeding, a selection of the most recent ALICE results on the medium global properties and on heavy-flavour and quarkonium production will be discussed