Each incoming beam particle may leave behind a beam remnant, which does not take part in the initial-state radiation or hard scattering process. If nothing else, the remnants need be reconstructed and connected to the rest of the event. In hadron-hadron collisions, the composite nature of the two incoming beam particles implies the additional possibility that several parton pairs undergo separate hard or semi-hard scatterings, `multiple interactions'. This may give a non-negligible contribution to the `underlying event' structure, and thus to the total multiplicity. Finally, in high-luminosity colliders, it is possible to have several collisions between beam particles in one and the same beam crossing, i.e. pile-up events, which further act to build up the general particle production activity that is to be observed by detectors. These three aspects are described in turn, with emphasis on the middle one, that of multiple interactions within a single hadron-hadron collision.
The main reference on the multiple interactions model is [Sjö87a].