Forward and small-x QCD physics results from CMS experiment at LHC

The Compact Muon Solenoid (CMS) is one of the two large, multi-purpose experiments at the Large Hadron Collider (LHC) at CERN. During the Run I Phase a large pp collision dataset has been collected and the CMS collaboration has explored measurements that shed light on a new era. Forward and small-$x$ quantum chromodynamics (QCD) physics measurements with CMS experiment covers a wide range of physics subjects. Some of highlights in terms of testing the very low-$x$ QCD, underlying event and multiple interaction characteristics, photon-mediated processes, jets with large rapidity separation at high pseudo-rapidities and the inelastic proton-proton cross section dominated by diffractive interactions are presented. Results are compared to Monte Carlo (MC) models with different parameter tunes for the description of the underlying event and to perturbative QCD calculations. The prominent role of multi-parton interactions has been confirmed in the semihard sector but no clear deviation from the standard DGLAP parton evolution due to BFKL has been observed. An outlook to the prospects at 13 TeV is given