We present results from studies of hard diffractive processes in
pbar p collisions at sqrt s = 1.8 TeV at the Tevatron using the CDF detector.
Diffractive events are identified by the characteristic signature of a
rapidity gap and/or by detecting a recoil antiproton with high forward
momentum.  Reactions studied include the diffractive production of W-bosons
and of two-jet (dijet) events, diffractive heavy quark production, and dijet
production by double-pomeron exchange.