We study Real and Deeply Virtual Compton Scattering in a model based on Regge trajectories and two-gluon exchange. In the kinematic regime of current experiments, the hadronic component of the outgoing real photon plays a major role. We analyze the spin structure of Compton scattering at large momentum transfer and give predictions for several spin asymmetries. In the DVCS channel, a fairly good agreement is obtained for the recently measured beam spin and charge asymmetries.