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At high energy, exclusive meson photo- and electro-production give access to the structure of hadronic matter. At low momentum transfers, the exchange of a few Regge trajectories leads to a comprehensive account of the cross-sections. Among these trajectories, which are related to the mass spectrum of families of mesons, the Pomeron plays an interesting role as it is related to glue-ball excitations. At high momentum transfers, the exchange of these collective excitations is expected to reduce to the exchange of their simplest (quark or gluon) components. However, contributions from unitarity rescattering cuts are relevant even at high energies. In the JLab energy range, the asymptotic regime, where the players in the game are current quarks and massless gluons has not been reached yet. One has to rely on more effective degrees of freedom adapted to the scale of the probe. A consistent picture, the "Partonic Non-Perturbative Regime", is emerging. The properties of its various components (dressed propagators, effective coupling constants, quark wave functions, shape of the Regge trajectories, etc.) provide us with various links to hadron properties. I will review the status of the field, will put in perspective the current achievements at JLab, SLAC and Hermes, and will assess future developments that are made possible by continuous electron beams at higher energies. [ABSTRACT FROM AUTHOR]