  We describe recent results from CMS and TOTEM on hard diffraction,
diffractive jets and jet gap jet events. We also give the first sensitivities
and limits on quartic anomalous couplings and axion-like particles at high mass
using the LHC as a $\gamma \gamma$ collider. The predicted sensitivities with
300 fb$^{-1}$ are better by two or three orders of magnitude compared to the
more standard methods at the LHC without measuring intact protons after
collision
