  The future opportunities for high-density QCD studies with ion and proton
beams at the LHC are presented. Four major scientific goals are identified: the
characterisation of the macroscopic long wavelength Quark-Gluon Plasma (QGP)
properties with unprecedented precision, the investigation of the microscopic
parton dynamics underlying QGP properties, the development of a unified picture
of particle production and QCD dynamics from small (pp) to large
(nucleus--nucleus) systems, the exploration of parton densities in nuclei in a
broad ($x$, $Q^2$) kinematic range and the search for the possible onset of
parton saturation. In order to address these scientific goals, high-luminosity
Pb-Pb and p-Pb programmes are considered as priorities for Runs 3 and 4,
complemented by high-multiplicity studies in pp collisions and a short run with
oxygen ions. High-luminosity runs with intermediate-mass nuclei, for example Ar
or Kr, are considered as an appealing case for extending the heavy-ion
programme at the LHC beyond Run 4. The potential of the High-Energy LHC to
probe QCD matter with newly-available observables, at twice larger
center-of-mass energies than the LHC, is investigated.
