  In this talk we review the models describing the hard diffractive production
of jets or more generally high-mass states in presence of rapidity gaps in
hadron-hadron and lepton-hadron collisions. By rapidity gaps we mean regions on
the lego plot in (pseudo)-rapidity and azimuthal angle where no hadrons are
produced, between the jet(s) and an elastically scattered hadron (single hard
diffraction) or between two jets (double hard diffraction).
