We report recent results on diffraction from the CDF experiment
at the Fermilab Tevatron p anti-p collider.  In events with multiple rapidity
gaps, we find that if a single gap survives, e.g. is not killed by products
of interactions between spectator partons, any additional gaps survive as
well.  Diffractive structure functions are studied in single-diffractive and
double-pomeron-exchange (DPE) dijet production.  Exclusive production of
dijets and of chi0_c in (DPE) dijet production.  Exclusive production of
dijets and of chi0_c in DPE have been studied as benchmark processes for
exclusive Higgs production at the LHC.