Small-x QCD and forward physics results from CMS

The CMS Collaboration has a comprehensive program of small-x QCD and forward physics measurements, which is supported by an excellent experimental coverage into the very forward phase space. Some of the highlights in terms of testing QCD at low transverse momenta ($p_T$) and at high pseudorapidities ($\eta$) with jets and charged particles are summarized. Also extremely rare processes, as the measurement of exclusive W-pair production in photon-photon collisions in proton-proton ($pp$) data are discussed. The range of physics results is complemented by studies of diffractive collisions, as well as of multi-parton interactions and soft-QCD phenomena. The measurement of the underlying event at different center-of-mass energies is another fundamental result presented. First results based on the data collected at 13 TeV are also discussed.