Exclusive production at the LHC

The exclusive production of dimuons, $pp \rightarrow p\mu^+\mu^-p$, is studied in a Monte Carlo simulation for $pp$ collisions at $7$~TeV and $14$~TeV. First, a continuum signal due to the QED process $\gamma\gamma \rightarrow \mu^{+}\mu^{-}$ is discussed, and then in the mass region $8 < m(\mu^+\mu^{-}) < 12$~GeV, search for the exclusive photoproduction of $\Upsilon$ mesons is described. Outlook for the studies of the exclusive processes with forward proton detectors are also presented.