Central Exclusive Particle Production at High Energy Hadron Colliders

We review the subject of central exclusive particle production at high energy hadron colliders. In particular we consider reactions of the type A + B -> A + X + B, where X is a fully specified system of particles that is well separated in rapidity from the outgoing beam particles. We focus on the case where the colliding particles are strongly interacting and mainly they will be protons (or antiprotons) as at the ISR, SppS, Tevatron and LHC. The data are surveyed and placed within the context of theoretical developments.