We present new results from studies on diffractive dijet production and exclusive production of dijet and diphoton obtained by the CDF Collaboration in proton-antiproton collisions at the Fermilab Tevatron.

Hard diffraction in events with dijets and rapidity gaps has been studied by D0 and CDF for three processes: hard color singlet exchange, hard single diffraction, and hard double pomeron exchange, using Tevatron [anti p]p data at [radical]s = 630 GeV and 1.8 TeV. Measurements of rates, [eta], E[sub T] and [radical]s dependencies are presented and comparisons made with predictions of several models.

Experimental results of hard single diffraction and double pomeron exchange studies at the Fermilab Tevatron p{bar p} collider are presented. Single diffraction results are compared with predictions from phenomenological models and expectations from results obtained in diffractive deep inelastic scattering experiments at the DESY ep collider HERA. Double pomeron exchange results are compared with corresponding single diffraction results to test factorization.

Experimental results in diffractive processes are summarized and a few notable characteristics described in terms of Quantum Chromodynamics. Exclusive dijet production is used to establish a benchmark for future experiments in the quest for diffractive Higgs production at the Large Hadron Collider. Using new data from the Tevatron and dedicated diffractive triggers, no excess over a smooth falling distribution for exclusive dijet events could be found. Stringent upper limits on the exclusive dijet production cross section are presented. The quark/gluon composition of dijet final states is used to provide additional hints on exclusive dijet production.

The diffractive program of the CDF Collaboration at the Fermilab Tevatron p{bar p} Collider is reviewed with emphasis on recent results from Run II at {radical}s = 1.96 TeV. Updated results on the x{sub B{sub j}} and Q{sup 2} 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 Q{sup 2} in the range 1 GeV{sup 2}

We review hard diffractive results and prospects at the Tevatron with an emphasis on factorization breaking in diffractive processes. Upper limits on the exclusive di-jet and {chi}{sub c}{sup 0} production cross sections at CDF and the status of the D0 Forward Proton Detectors are discussed.