Abstract We present the capabilities of the CMS experiment to explore the heavy-ion physics program of the CERN Large Hadron Collider (LHC). Collisions of lead nuclei at energies up to s N N = 5.5 TeV will probe quark and gluon matter at unprecedented values of energy density. The prime goal of this research is to study the fundamental theory of the strong interaction (QCD) in extreme conditions of temperature, density and parton momentum fraction. We give an overview of the potential of CMS to carry out a full set of representative Pb-Pb measurements both in “soft” and “hard” regimes. Measurements include “bulk” observables — charged hadron multiplicity, low- p T inclusive identified hadron spectra and elliptic flow — which provide information on the collective properties of the system; as well as perturbative processes — such as quarkonia, heavy quarks, jets, γ–jet and high p T hadrons — which yield “tomographic” information on the hottest and densest phases of the reaction. In addition, reference measurements that have been performed on early p+p collision data will be reviewed.