  In this talk we present a selection of forward physics results recently
obtained with the run-1 and run-2 LHC data by the CMS, LHCf and TOTEM
experiments. The status of the very forward LHC proton spectrometer, CT-PPS, is
discussed: emphasis is given to the physics potential of CT-PPS and to the
analyses that are currently ongoing with the data collected in 2016. Very
recent forward measurements obtained with the LHCf and the CMS-CASTOR
calorimeter are then addressed. In particular, CMS measured the inclusive
energy spectrum in the very forward direction for proton-proton collisions at a
center-of-mass energy of 13 TeV and the jet cross sections for p+Pb collisions
at 5.02 TeV. The LHCf experiment has instead recently published the inclusive
energy spectra of forward photons for pp collisions at 13 TeV. Finally, the new
measurements of the total, elastic and inelastic cross sections obtained by the
TOTEM collaboration at 2.76 and 13 TeV center of mass energy are presented.
