  We consider the central exclusive production of the $p\bar{p}$ in the
continuum and via resonances in proton-proton collisions at high energies. We
discuss the diffractive mechanism calculated within the tensor-pomeron approach
including pomeron, odderon, and reggeon exchanges. The theoretical results are
discussed in the context of existing WA102 and ISR experimental data and
predictions for planned or current experiments at the RHIC and the LHC are
presented. The distribution in ${\rm y}_{diff}$, the rapidity distance between
proton and antiproton, is particularly interesting. We find a dip at ${\rm
y}_{diff} = 0$ for the $p \bar{p}$ production, in contrast to the
$\pi^{+}\pi^{-}$ and $K^{+}K^{-}$ production. We predict also the $p \bar{p}$
invariant mass distribution to be less steep than for the pairs of pseudoscalar
mesons. We argue that these specific differences for the $p \bar{p}$ production
with respect to the pseudoscalar meson pair production can be attributed to the
proper treatment of the spin of produced particles. We discuss asymmetries that
are due to the interference of $C=+1$ and $C=-1$ amplitudes of $p \bar{p}$
production. We have also calculated the cross section for the $pp \to pp
\Lambda \overline{\Lambda}$ reaction. Here, the cross section is smaller but
the characteristic feature for $d\sigma/d{\rm y}_{diff}$ is predicted to be
similar to $p \bar{p}$ production. The presence of resonances in the $p \bar p$
channel may destroy the dip at ${\rm y}_{diff} = 0$. This opens the possibility
to study diffractively produced resonances. We discuss the observables suited
for this purpose.
