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. We outline a model
which incorporates these features. Finally, we discuss what the most recent LHC
measurements in the soft domain imply for the model.Comment: 12 pages, 5 figures. Presented at Linear Collider 2011: Understanding
QCD at Linear Colliders in searching for old and new physics, 12-16 September
2011, ECT*, Trento, Ital
