We report recent results on diffraction and exclusive production
obtained by the CDF collaboration in p anti-p collisions at the Fermilab
Tevatron collider at s**(1/2) = 1.96 TeV.  A measurement of the Q2 and t
dependence of the diffractive structure function extracted from diffractive
dijet production in the range of 102 < 104 GeV2 and |t| < 1 GeV2 is
presented.  Results are also presented for exclusive e+ e-, gamma gamma,
and dijet production.