Measurements of soft and hard diffractive processes have been performed at the Tevatron pp collider during the past decade. Diffractive events are studied by means of identification of one or more rapidity gaps and/or a leading antiproton. Here, results are discussed within the Tevatron data and compared to those obtained at the HERA ep collider. The traditional "pomeron" is described within the framework of QCD and the issues discussed include pomeron structure, diffractive cross section factorization, and universality of rapidity gap formation. Exclusive dijet and low-mass state production in double-pomeron exchange processes, including predictions for Higgs production at the LHC from dijet measurements at the Tevatron.
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