  We discuss central exclusive diffractive dihadron production in proton-proton
collisions at high energies. The calculation is based on a tensor pomeron model
and the amplitudes for the processes are formulated in an effective
field-theoretic approach. We include a purely diffractive dipion continuum, and
the scalar and tensor resonances decaying into the $\pi^{+} \pi^{-}$ pairs as
well as the photoproduction contributions ($\rho^{0}$, Drell-S\"oding). We
discuss how two pomerons couple to tensor meson $f_{2}(1270)$ and the
interference effects of the scalar and tensor resonances and the dipion
continuum. The theoretical results are compared with existing CDF and CMS
experimental data. We discuss also the Drell-Hiida-Deck type mechanism with
centrally produced $\rho^{0}$ meson associated with a very forward/backward
$\pi N$ system. For the $pp \to pp \pi^{+} \pi^{-} \pi^{+} \pi^{-}$ reaction we
consider both the $\sigma \sigma$ and $\rho \rho$ contributions as well as the
triple Regge exchange mechanism. Predictions for planned or being carried out
experiments (STAR, ALICE, ATLAS, CMS) are presented. We show the influence of
the experimental cuts on the integrated cross section and on various
differential distributions for outgoing particles.
