I will overview the experimental capabilities on small-x and QGP physics accessible with the CMS detector in p+p and Pb+Pb collisions in the multi-TeV regime at CERN LHC. Expectations on hard probes cross-sections (jets, quarkonia, ...) will be given for different physics scenarios (gluon saturation, QGP w/ initial temperatures in the ~1 GeV range, ...) based on realistic luminosities for the first two p+p and Pb+Pb runs. Emphasis will be put on the rich forward physics capabilities of the CMS setup (CASTOR, TOTEM, HCAL, ZDC detectors ...) and other interesting research topics (connections to ultra-high-energy cosmic rays physics, diffractive Higgs production in p+p, ...) will be also mentioned.