  The H1 and Zeus collaborations have measured the inclusive diffractive DIS
cross section ep -> eXp and these measurements are in good agreement within a
normalisation uncertainty. Diffractive parton density functions (DPDFs) have
been extracted from NLO QCD fits to these data and the predictions of these
DPDFs compare well with measurements of diffractive dijets in DIS, proving the
validity of the factorisation approximations used in their extraction. The
inclusive and dijet data are then used in a combined fit to constrain the
diffractive singlet and gluon with good precision over the full phase space.
The predictions of DPDFs are compared to diffractive dijets in photoproduction
where the issue of survival probability in a hadron-hadron environment can be
studied. Finally, exclusive diffractive vector meson production and deeply
virtual Compton scattering have also been studied; the results compare
reasonably well with the expectations of QCD and in particular with GPD models.
