  The heavy ion (HI) physics program has proven to be an essential part of the
overall physics program at the Large Hadron Collider at CERN. Its main purpose
has been to provide a detailed characterization of the quark-gluon plasma
(QGP), a deconfined state of quarks and gluons created in high-energy
nucleus-nucleus collisions. From the start of the LHC HI program with lead-lead
collisions, the CMS Collaboration has performed measurements using additional
data sets in different center-of-mass energies with xenon-xenon, proton-lead,
and proton-proton collisions. A broad collection of observables related to
high-density quantum chromodynamics (QCD), precision quantum electrodynamics
(QED), and even novel searches of phenomena beyond the standard model (BSM)
have been studied. Major advances toward understanding the macroscopic and
microscopic QGP properties were achieved at the highest temperature reached in
the laboratory and for vanishingly small values of the baryon chemical
potential. This article summarizes key QCD, QED, as well as BSM physics,
results of the CMS HI program for the LHC Runs 1 (2010-2013) and 2 (2015-2018).
It reviews findings on the partonic content of nuclei and properties of the QGP
and describes the surprising QGP-like effects in collision systems smaller than
lead-lead or xenon-xenon. In addition, it outlines the scientific case of using
ultrarelativistic HI collisions in the coming decades to characterize the QGP
with unparalleled precision and to probe novel fundamental physics phenomena.
