CDF results on hard diffraction and rapidity gap physics

We review published rapidity gap results on diffractive W and dijet production and discuss new results on diffractive b and J/{psi} production. The diffractive structure function of the proton obtained from Roman pot dijet data is presented and com- pared with expectations based on the diffractive parton densities extracted from DIS at HERA. Also presented are results on dijet production in double Pomeron exchange. Finally, we review hard double-diffractive results (rapidity gaps between jets) and present new results on soft double diffraction