Review of results on forward physics and diffraction by CMS

Results by the CMS Collaboration on forward physics, diffraction, and physics in the small-$x$ limit of quantum chromodynamics (QCD), are presented. In particular, results on azimuthal angle decorrelations between two jets in events where two outermost jets are separated by a large rapidity interval are discussed. In addition, results based on the production of two jets separated by a large rapidity gap (interval void of radiation) are presented. These dijet production processes are expected to be sensitive to Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution effects. We highlight results on inclusive forward jet production and on exclusive vector meson production in proton-lead collisions, which access gluon densities in the small-$x$ and $Q^2$ where saturation effects may play a role. A summary of results on underlying event activity studies based on inclusive $Z$ boson production, charged particle spectra in minimum bias events, and energy density in forward pseudorapidities is presented. These studies provide valuable inputs for Monte Carlo event generator tuning, and test predictions based on perturbative and non-perturbative QCD techniques.