  Exclusive and diffractive physics measurements are important for the better
understanding of the non-perturbative regime of QCD. Two recent results of the
CMS experiment is presented in this paper. The total and differential cross
sections of central exclusive $\pi^+\pi^-$ production are measured at 5.02 and
13 TeV in the $p_{\mathrm{T}}(\pi) > 0.2~$GeV/$c$ and $|\eta(\pi)| < 2.4$
kinematic region. The invariant mass distribution is fitted by the sum of a
continuum and four interfering relativistic Breit-Wigner functions. In the
second part of the paper the measurement of the single diffractive dijets is
presented, which are studied by using proton tagging capabilities of the TOTEM
analysis. A joint CMS-TOTEM study is carried out and the total and differential
cross sections are measured in the $0.03 < |t| < 1.0~$GeV$^2$ and $0 < \xi <
0.1$ kinematic region.
