  We discuss the qualitative features of the recent data on multiparticle
production observed at the LHC. The tolerable agreement with Monte Carlos based
on LO DGLAP evolution indicates that there is no qualitative difference between
`hard' and `soft' interactions; and that a perturbative QCD approach may be
extended into the soft domain. However, in order to describe the data, these
Monte Carlos need an additional infrared cutoff k_min with a value k_min ~ 2-3
GeV which is not small, and which increases with collider energy. Here we
explain the physical origin of the large k_min. Using an alternative model
which matches the `soft' high-energy hadron interactions smoothly on to
perturbative QCD at small x, we demonstrate that this effective cutoff k_min is
actually due to the strong absorption of low k_t partons. The model embodies
the main features of the BFKL approach, including the diffusion in transverse
momenta, lnk_t, and an intercept consistent with resummed next-to-leading log
corrections. Moreover, the model uses a two-channel eikonal framework, and
includes the contributions from the multi-Pomeron exchange diagrams, both
non-enhanced and enhanced. The values of a small number of physically-motivated
parameters are chosen to reproduce the available total, elastic and proton
dissociation cross section (pre-LHC) data. Predictions are made for the LHC,
and the relevance to ultra-high-energy cosmic rays is briefly discussed. The
low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are
calculated in this framework, using the parameters which describe the
high-energy pp and p\bar{p} `soft' data. Comparison with the PDFs obtained from
the global parton analyses of deep inelastic and related `hard' scattering
data, and from diffractive deep inelastic data looks encouraging.
