  We discuss how the main features of high-energy `soft' and `semihard' pp
collisions may be described in terms of parton cascades and multi-Pomeron
exchange. The interaction between Pomerons produces an effective infrared
cutoff, k_{sat}, by the absorption of low k_t partons. This provides the
possibility of extending the parton approach, used for `hard' processes, to
also describe high-energy soft and semihard interactions. In particular, the
presence of the cutoff k_{sat}, which increases with collider energy, means
that the production and hadronization of minijets with p_t\gapproxeq k_{sat}
are the main source of the soft secondaries. We propose several measurements
which can be made at the LHC, that can further illuminate our understanding of
the mechanism which drives the soft and semihard interactions. We show that the
structure of Pomeron-Pomeron interactions may be studied in
Double-Pomeron-Exchange processes and in the p_t distributions of secondaries
near the edge of large rapidity gaps. The so-called `ridge effect' is another
manifestation of the interaction of two partonic cascades.
