`The phenomenology of central exclusive production' Abstract: Central exclusive production (CEP) is a hadron-hadron interaction where a particle (or system of particles) X is produced while the hadrons remain intact after the collision, scattering at some small angle from the beam axis. While experimentally it represents a potentially clean environment in which to observe and measure the properties of new and Standard Model particles, on the theory side it provides a novel probe of QCD and diffractive physics. In this talk I will look at the CEP of systems with sufficiently low masses that the observation of these processes is already possible at the Tevatron, RHIC and in LHC low luminosity runs, as well as discussing the potential to probe Higgs and new physics at the LHC. I will in particular discuss, in different levels of detail, the theoretical and phenomenological aspects of light meson pair (pi+pi-, K+K-, eta(`)eta(`)...), chi_c, diphoton, Higgs, and SUSY particle production.