  We review some selected results of the tensor-pomeron and vector-odderon
model of soft high-energy proton-proton scattering and central exclusive
production of meson and baryon pairs in proton-proton collisions. We discuss
the theoretical aspects of this approach and consider the phenomenological
implications in a variety of processes at high energies, comparing to existing
experimental data. We consider the diffractive dipion and dikaon production
including the continuum and the dominant scalar and tensor resonance
contributions as well as the photoproduction processes. The theoretical results
are compared with existing CDF experimental data and predictions for planned or
current LHC experiments, ALICE, ATLAS, CMS, LHCb are presented.
