  We review two inter-related topics. First, we consider the behaviour of
"soft" scattering observables, such as sigma_{tot}, dsigma_{el}/dt,
dsigma_{SD}/dtdM^2, particle multiplicities etc., at high-energy
proton-(anti)proton colliders. We emphasize the sizeable effects of absorption
on high-energy `soft' processes, and, hence, the necessity to include
multi-Pomeron-Pomeron interactions in the usual multi-channel eikonal
description. We describe a multi-component model which has been tuned to the
available data for soft processes in the CERN-ISR to Tevatron energy range, and
which therefore allows predictions to be made for `soft' observables at the
LHC. The second topic concerns the calculation of the rate of exclusive
processes of the form pp --> p+A+p at high energy colliders, where A is a heavy
system. In particular, we discuss the survival probability of the rapidity gaps
(denoted by the + signs) to both eikonal and enhanced soft rescattering
effects. At the LHC energy, the most topical case is when A is a Higgs boson.
At the Tevatron, measurements have been made for the exclusive diffractive
production of various systems: A being either gamma-gamma, dijet, or a chi_c
meson. We compare the observed rates with the expectations. Finally, we
describe how predictions for exclusive processes may be checked in the early
runs of the LHC.
