  `Soft' high-energy interactions are clearly important in pp collisions.
Indeed, these events are dominant by many orders of magnitude, and about 40%
are of diffractive origin; that is, due to elastic scattering or proton
dissociation. Moreover, soft interactions unavoidably give an underlying
component to the rare `hard' events, from which we hope to extract new physics.
Here, we discuss how to quantify this contamination. First we present a brief
introduction to diffraction. We emphasize the different treatment required for
proton dissociation into low- and high-mass systems; the former requiring a
multichannel eikonal approach, and the latter the computation of triple-Pomeron
diagrams with multi-Pomeron corrections. Then we give an overview of the
Pomeron, and explain how the QCD (BFKL-type) Pomeron is the natural object to
continue from the `hard' to the `soft' domain. In this way we can obtain a
partonic description of soft interactions. We introduce the so-called KMR
model, based on this partonic approach, which includes absorptive multi-Pomeron
corrections that become increasingly important as we proceed further into the
soft domain. This model is able to describe total, elastic and proton
dissociation data, and to predict the survival probability of large rapidity
gaps to soft rescattering --- in terms of a few physically-motivated
parameters. However, more differential phenomena, such as single particle p_t
distributions, can only be satisfactorily described if hadronization effects
are included. This is achieved by incorporating the KMR analytic approach into
the SHERPA Monte Carlo framework. It allows a description of soft physics and
diffraction, together with jet physics, in a coherent, self-consistent way. We
outline the structure, and show a few results, of this Monte Carlo, which we
call SHRiMPS, for reasons which will become clear.
