Soft physics at the LHC

We recall the main features of the Regge approach used to understand soft interactions at LHC and higher energies. Unitarity tames the power growth of the elastic proton-proton scattering amplitude with energy, and leads to the migration of the secondary particles produced in high-energy proton-proton collisions to larger transverse momenta. We discuss, in qualitative terms, the role of processes containing large rapidity gaps (LRG), and the probability that the gaps survive population by secondaries produced in additional soft interactions. We explain how the Regge diagram corresponding to a LRG event simultaneously describes events with different (single, double, etc.) particle density in the same rapidity interval. We show that the role of these, enhanced, multi-Pomeron diagrams can be studied by measuring multiplicity fluctuations and long-range rapidity correlations between secondaries produced at the Tevatron and the LHC. Finally, we make a list of the characteristic features of the multi-Pomeron description of soft interactions that may be observed at the high energies accessible at the Tevatron and the LHC.