Experimental results from the CDF experiment at the Tevatron in
p anti-p collisions at s**(1/2) = 1.96 TeV are presented on the diffractive
structure function at different values of the exchanged momentum transfer
squared in the range 0 < Q2 < 10,000 GeV2, on the four-momentum transfer
|t| distribution in the region 0 < |t| < 1 GeV2 for both soft and hard
diffractive events up to Q2 \approx 4,500 GeV2, and on the first
experimental evidence of exclusive production in both dijet and diphoton
events.  A novel technique to align the Roman Pot detectors is also
presented.