The diffractive program of the CDF Collaboration at the Fermilab
Tevatron p anti-p Collider is reviewed with emphasis on recent results from Run
II at s**(1/2) = 1.96 TeV.  Updated results on the X_Bj and Q2 dependence of
the diffractive structure function obtained from dijet production, and on
the slope parameter of the t-distribution of diffractive events as a
function of Q2 in the range 1 GeV2 < Q2 < 104 GeV2, are presented and
compared with theoretical expectations.  Results on cross sections for
exclusive dijet and diphoton production are also presented and used to
calibrate theoretical estimates for exclusive Higgs production at the Large
Hadron Collider.